https://www.math.wisc.edu/wiki/api.php?action=feedcontributions&user=Admin&feedformat=atomUW-Math Wiki - User contributions [en]2020-02-25T12:44:50ZUser contributionsMediaWiki 1.30.1https://www.math.wisc.edu/wiki/index.php?title=Probability_Seminar&diff=17259Probability Seminar2019-04-01T16:06:35Z<p>Admin: /* April 11, Eviatar Procaccia, Texas A&M */</p>
<hr />
<div>__NOTOC__<br />
<br />
= Spring 2019 =<br />
<br />
<b>Thursdays in 901 Van Vleck Hall at 2:25 PM</b>, unless otherwise noted. <br />
<b>We usually end for questions at 3:15 PM.</b><br />
<br />
If you would like to sign up for the email list to receive seminar announcements then please send an email to <br />
[mailto:join-probsem@lists.wisc.edu join-probsem@lists.wisc.edu]<br />
<br />
<br />
<br />
== January 31, [https://www.math.princeton.edu/people/oanh-nguyen Oanh Nguyen], [https://www.math.princeton.edu/ Princeton] ==<br />
<br />
Title: '''Survival and extinction of epidemics on random graphs with general degrees'''<br />
<br />
Abstract: We establish the necessary and sufficient criterion for the contact process on Galton-Watson trees (resp. random graphs) to exhibit the phase of extinction (resp. short survival). We prove that the survival threshold $\lambda_1$ for a Galton-Watson tree is strictly positive if and only if its offspring distribution has an exponential tail, settling a conjecture by Huang and Durrett. On the random graph with degree distribution $D$, we show that if $D$ has an exponential tail, then for small enough $\lambda$ the contact process with the all-infected initial condition survives for polynomial time with high probability, while for large enough $\lambda$ it runs over exponential time with high probability. When $D$ is subexponential, the contact process typically displays long survival for any fixed $\lambda>0$.<br />
Joint work with Shankar Bhamidi, Danny Nam, and Allan Sly.<br />
<br />
== <span style="color:red"> Wednesday, February 6 at 4:00pm in Van Vleck 911</span> , [https://lc-tsai.github.io/ Li-Cheng Tsai], [https://www.columbia.edu/ Columbia University] ==<br />
<br />
Title: '''When particle systems meet PDEs'''<br />
<br />
Abstract: Interacting particle systems are models that involve many randomly evolving agents (i.e., particles). These systems are widely used in describing real-world phenomena. In this talk we will walk through three facets of interacting particle systems, namely the law of large numbers, random fluctuations, and large deviations. Within each facet, I will explain how Partial Differential Equations (PDEs) play a role in understanding the systems..<br />
<br />
== February 7, [http://www.math.cmu.edu/~yug2/ Yu Gu], [https://www.cmu.edu/math/index.html CMU] ==<br />
<br />
Title: '''Fluctuations of the KPZ equation in d\geq 2 in a weak disorder regime'''<br />
<br />
Abstract: We will discuss some recent work on the Edwards-Wilkinson limit of the KPZ equation with a small coupling constant in d\geq 2.<br />
<br />
== February 14, [https://www.math.wisc.edu/~seppalai/ Timo Seppäläinen], UW-Madison==<br />
<br />
Title: '''Geometry of the corner growth model'''<br />
<br />
Abstract: The corner growth model is a last-passage percolation model of random growth on the square lattice. It lies at the nexus of several branches of mathematics: probability, statistical physics, queueing theory, combinatorics, and integrable systems. It has been studied intensely for almost 40 years. This talk reviews properties of the geodesics, Busemann functions and competition interfaces of the corner growth model, and presents some new qualitative and quantitative results. Based on joint projects with Louis Fan (Indiana), Firas Rassoul-Agha and Chris Janjigian (Utah).<br />
<br />
== February 21, [https://people.kth.se/~holcomb/ Diane Holcomb], KTH ==<br />
<br />
<br />
Title: '''On the centered maximum of the Sine beta process'''<br />
<br />
<br />
Abstract: There has been a great deal or recent work on the asymptotics of the maximum of characteristic polynomials or random matrices. Other recent work studies the analogous result for log-correlated Gaussian fields. Here we will discuss a maximum result for the centered counting function of the Sine beta process. The Sine beta process arises as the local limit in the bulk of a beta-ensemble, and was originally described as the limit of a generalization of the Gaussian Unitary Ensemble by Valko and Virag with an equivalent process identified as a limit of the circular beta ensembles by Killip and Stoiciu. A brief introduction to the Sine process as well as some ideas from the proof of the maximum will be covered. This talk is on joint work with Elliot Paquette.<br />
<br />
== Probability related talk in PDE Geometric Analysis seminar: <br> Monday, February 22 3:30pm to 4:30pm, Van Vleck 901, Xiaoqin Guo, UW-Madison ==<br />
<br />
Title: Quantitative homogenization in a balanced random environment<br />
<br />
Abstract: Stochastic homogenization of discrete difference operators is closely related to the convergence of random walk in a random environment (RWRE) to its limiting process. In this talk we discuss non-divergence form difference operators in an i.i.d random environment and the corresponding process—a random walk in a balanced random environment in the integer lattice Z^d. We first quantify the ergodicity of the environment viewed from the point of view of the particle. As consequences, we obtain algebraic rates of convergence for the quenched central limit theorem of the RWRE and for the homogenization of both elliptic and parabolic non-divergence form difference operators. Joint work with J. Peterson (Purdue) and H. V. Tran (UW-Madison).<br />
<br />
== <span style="color:red"> Wednesday, February 27 at 1:10pm</span> [http://www.math.purdue.edu/~peterson/ Jon Peterson], [http://www.math.purdue.edu/ Purdue] ==<br />
<br />
<br />
<div style="width:520px;height:50px;border:5px solid black"><br />
<b><span style="color:red">&emsp; Please note the unusual day and time. <br />
&emsp; </span></b><br />
</div><br />
<br />
Title: '''Functional Limit Laws for Recurrent Excited Random Walks'''<br />
<br />
Abstract:<br />
<br />
Excited random walks (also called cookie random walks) are model for self-interacting random motion where the transition probabilities are dependent on the local time at the current location. While self-interacting random walks are typically very difficult to study, many results for (one-dimensional) excited random walks are remarkably explicit. In particular, one can easily (by hand) calculate a parameter of the model that will determine many features of the random walk: recurrence/transience, non-zero limiting speed, limiting distributions and more. In this talk I will prove functional limit laws for one-dimensional excited random walks that are recurrent. For certain values of the parameters in the model the random walks under diffusive scaling converge to a Brownian motion perturbed at its extremum. This was known previously for the case of excited random walks with boundedly many cookies per site, but we are able to generalize this to excited random walks with periodic cookie stacks. In this more general case, it is much less clear why perturbed Brownian motion should be the correct scaling limit. This is joint work with Elena Kosygina.<br />
<br />
<!-- == March 7, TBA == --><br />
<br />
<!-- == March 14, TBA == --><br />
<br />
== March 21, Spring Break, No seminar ==<br />
<br />
== March 28, [https://www.math.wisc.edu/~shamgar/ Shamgar Gurevitch] [https://www.math.wisc.edu/ UW-Madison]==<br />
<br />
Title: '''Harmonic Analysis on GLn over finite fields, and Random Walks'''<br />
<br />
Abstract: There are many formulas that express interesting properties of a group G in terms of sums over its characters. For evaluating or estimating these sums, one of the most salient quantities to understand is the ''character ratio'': <br />
<br />
$$<br />
\text{trace}(\rho(g))/\text{dim}(\rho),<br />
$$<br />
<br />
for an irreducible representation $\rho$ of G and an element g of G. For example, Diaconis and Shahshahani stated a formula of this type for analyzing G-biinvariant random walks on G. It turns out that, for classical groups G over finite fields (which provide most examples of finite simple groups), there is a natural invariant of representations that provides strong information on the character ratio. We call this invariant ''rank''. This talk will discuss the notion of rank for $GL_n$ over finite fields, and apply the results to random walks. This is joint work with Roger Howe (Yale and Texas AM).<br />
<br />
== April 4, [https://www.math.wisc.edu/~pmwood/ Philip Matchett Wood], [http://www.math.wisc.edu/ UW-Madison] ==<br />
<br />
Title: '''Outliers in the spectrum for products of independent random matrices'''<br />
<br />
Abstract: For fixed positive integers m, we consider the product of m independent n by n random matrices with iid entries as in the limit as n tends to infinity. Under suitable assumptions on the entries of each matrix, it is known that the limiting empirical distribution of the eigenvalues is described by the m-th power of the circular law. Moreover, this same limiting distribution continues to hold if each iid random matrix is additively perturbed by a bounded rank deterministic error. However, the bounded rank perturbations may create one or more outlier eigenvalues. We describe the asymptotic location of the outlier eigenvalues, which extends a result of Terence Tao for the case of a single iid matrix. Our methods also allow us to consider several other types of perturbations, including multiplicative perturbations. Joint work with Natalie Coston and Sean O'Rourke.<br />
<br />
== April 11, [https://sites.google.com/site/ebprocaccia/ Eviatar Procaccia], [http://www.math.tamu.edu/index.html Texas A&M] ==<br />
<br />
'''Title: Stabilization of Diffusion Limited Aggregation in a Wedge.''' <br />
<br />
Abstract: We prove a discrete Beurling estimate for the harmonic measure in a wedge in $\mathbf{Z}^2$, and use it to show that Diffusion Limited Aggregation (DLA) in a wedge of angle smaller than $\pi/4$ stabilizes. This allows to consider the infinite DLA and questions about the number of arms, growth and dimension. I will present some conjectures and open problems.<br />
<br />
== April 18, [https://services.math.duke.edu/~agazzi/index.html Andrea Agazzi], [https://math.duke.edu/ Duke] ==<br />
<br />
== April 25, [https://www.brown.edu/academics/applied-mathematics/kavita-ramanan Kavita Ramanan], [https://www.brown.edu/academics/applied-mathematics/ Brown] ==<br />
<br />
== April 26, Colloquium, [https://www.brown.edu/academics/applied-mathematics/kavita-ramanan Kavita Ramanan], [https://www.brown.edu/academics/applied-mathematics/ Brown] ==<br />
<br />
<!-- == April 26, TBA == --><br />
<br />
== May 2, TBA ==<br />
<br />
<br />
<!--<br />
==<span style="color:red"> Friday, August 10, 10am, B239 Van Vleck </span> András Mészáros, Central European University, Budapest ==<br />
<br />
<br />
Title: '''The distribution of sandpile groups of random regular graphs'''<br />
<br />
Abstract:<br />
We study the distribution of the sandpile group of random <math>d</math>-regular graphs. For the directed model we prove that it follows the Cohen-Lenstra heuristics, that is, the probability that the <math>p</math>-Sylow subgroup of the sandpile group is a given <math>p</math>-group <math>P</math>, is proportional to <math>|\operatorname{Aut}(P)|^{-1}</math>. For finitely many primes, these events get independent in limit. Similar results hold for undirected random regular graphs, there for odd primes the limiting distributions are the ones given by Clancy, Leake and Payne.<br />
<br />
Our results extends a recent theorem of Huang saying that the adjacency matrices of random <math>d</math>-regular directed graphs are invertible with high probability to the undirected case.<br />
<br />
<br />
==September 20, [http://math.columbia.edu/~hshen/ Hao Shen], [https://www.math.wisc.edu/ UW-Madison] ==<br />
<br />
Title: '''Stochastic quantization of Yang-Mills'''<br />
<br />
Abstract:<br />
"Stochastic quantization” refers to a formulation of quantum field theory as stochastic PDEs. Interesting progress has been made these years in understanding these SPDEs, examples including Phi4 and sine-Gordon. Yang-Mills is a type of quantum field theory which has gauge symmetry, and its stochastic quantization is a Yang-Mills flow perturbed by white noise.<br />
In this talk we start by an Abelian example where we take a symmetry-preserving lattice regularization and study the continuum limit. We will then discuss non-Abelian Yang-Mills theories and introduce a symmetry-breaking smooth regularization and restore the symmetry using a notion of gauge-equivariance. With these results we can construct dynamical Wilson loop and string observables. Based on [S., arXiv:1801.04596] and [Chandra,Hairer,S., work in progress].<br />
<br />
--><br />
<br />
== ==<br />
<br />
[[Past Seminars]]</div>Adminhttps://www.math.wisc.edu/wiki/index.php?title=Probability_Seminar&diff=17258Probability Seminar2019-04-01T16:06:23Z<p>Admin: /* April 11, Eviatar Procaccia, Texas A&M */</p>
<hr />
<div>__NOTOC__<br />
<br />
= Spring 2019 =<br />
<br />
<b>Thursdays in 901 Van Vleck Hall at 2:25 PM</b>, unless otherwise noted. <br />
<b>We usually end for questions at 3:15 PM.</b><br />
<br />
If you would like to sign up for the email list to receive seminar announcements then please send an email to <br />
[mailto:join-probsem@lists.wisc.edu join-probsem@lists.wisc.edu]<br />
<br />
<br />
<br />
== January 31, [https://www.math.princeton.edu/people/oanh-nguyen Oanh Nguyen], [https://www.math.princeton.edu/ Princeton] ==<br />
<br />
Title: '''Survival and extinction of epidemics on random graphs with general degrees'''<br />
<br />
Abstract: We establish the necessary and sufficient criterion for the contact process on Galton-Watson trees (resp. random graphs) to exhibit the phase of extinction (resp. short survival). We prove that the survival threshold $\lambda_1$ for a Galton-Watson tree is strictly positive if and only if its offspring distribution has an exponential tail, settling a conjecture by Huang and Durrett. On the random graph with degree distribution $D$, we show that if $D$ has an exponential tail, then for small enough $\lambda$ the contact process with the all-infected initial condition survives for polynomial time with high probability, while for large enough $\lambda$ it runs over exponential time with high probability. When $D$ is subexponential, the contact process typically displays long survival for any fixed $\lambda>0$.<br />
Joint work with Shankar Bhamidi, Danny Nam, and Allan Sly.<br />
<br />
== <span style="color:red"> Wednesday, February 6 at 4:00pm in Van Vleck 911</span> , [https://lc-tsai.github.io/ Li-Cheng Tsai], [https://www.columbia.edu/ Columbia University] ==<br />
<br />
Title: '''When particle systems meet PDEs'''<br />
<br />
Abstract: Interacting particle systems are models that involve many randomly evolving agents (i.e., particles). These systems are widely used in describing real-world phenomena. In this talk we will walk through three facets of interacting particle systems, namely the law of large numbers, random fluctuations, and large deviations. Within each facet, I will explain how Partial Differential Equations (PDEs) play a role in understanding the systems..<br />
<br />
== February 7, [http://www.math.cmu.edu/~yug2/ Yu Gu], [https://www.cmu.edu/math/index.html CMU] ==<br />
<br />
Title: '''Fluctuations of the KPZ equation in d\geq 2 in a weak disorder regime'''<br />
<br />
Abstract: We will discuss some recent work on the Edwards-Wilkinson limit of the KPZ equation with a small coupling constant in d\geq 2.<br />
<br />
== February 14, [https://www.math.wisc.edu/~seppalai/ Timo Seppäläinen], UW-Madison==<br />
<br />
Title: '''Geometry of the corner growth model'''<br />
<br />
Abstract: The corner growth model is a last-passage percolation model of random growth on the square lattice. It lies at the nexus of several branches of mathematics: probability, statistical physics, queueing theory, combinatorics, and integrable systems. It has been studied intensely for almost 40 years. This talk reviews properties of the geodesics, Busemann functions and competition interfaces of the corner growth model, and presents some new qualitative and quantitative results. Based on joint projects with Louis Fan (Indiana), Firas Rassoul-Agha and Chris Janjigian (Utah).<br />
<br />
== February 21, [https://people.kth.se/~holcomb/ Diane Holcomb], KTH ==<br />
<br />
<br />
Title: '''On the centered maximum of the Sine beta process'''<br />
<br />
<br />
Abstract: There has been a great deal or recent work on the asymptotics of the maximum of characteristic polynomials or random matrices. Other recent work studies the analogous result for log-correlated Gaussian fields. Here we will discuss a maximum result for the centered counting function of the Sine beta process. The Sine beta process arises as the local limit in the bulk of a beta-ensemble, and was originally described as the limit of a generalization of the Gaussian Unitary Ensemble by Valko and Virag with an equivalent process identified as a limit of the circular beta ensembles by Killip and Stoiciu. A brief introduction to the Sine process as well as some ideas from the proof of the maximum will be covered. This talk is on joint work with Elliot Paquette.<br />
<br />
== Probability related talk in PDE Geometric Analysis seminar: <br> Monday, February 22 3:30pm to 4:30pm, Van Vleck 901, Xiaoqin Guo, UW-Madison ==<br />
<br />
Title: Quantitative homogenization in a balanced random environment<br />
<br />
Abstract: Stochastic homogenization of discrete difference operators is closely related to the convergence of random walk in a random environment (RWRE) to its limiting process. In this talk we discuss non-divergence form difference operators in an i.i.d random environment and the corresponding process—a random walk in a balanced random environment in the integer lattice Z^d. We first quantify the ergodicity of the environment viewed from the point of view of the particle. As consequences, we obtain algebraic rates of convergence for the quenched central limit theorem of the RWRE and for the homogenization of both elliptic and parabolic non-divergence form difference operators. Joint work with J. Peterson (Purdue) and H. V. Tran (UW-Madison).<br />
<br />
== <span style="color:red"> Wednesday, February 27 at 1:10pm</span> [http://www.math.purdue.edu/~peterson/ Jon Peterson], [http://www.math.purdue.edu/ Purdue] ==<br />
<br />
<br />
<div style="width:520px;height:50px;border:5px solid black"><br />
<b><span style="color:red">&emsp; Please note the unusual day and time. <br />
&emsp; </span></b><br />
</div><br />
<br />
Title: '''Functional Limit Laws for Recurrent Excited Random Walks'''<br />
<br />
Abstract:<br />
<br />
Excited random walks (also called cookie random walks) are model for self-interacting random motion where the transition probabilities are dependent on the local time at the current location. While self-interacting random walks are typically very difficult to study, many results for (one-dimensional) excited random walks are remarkably explicit. In particular, one can easily (by hand) calculate a parameter of the model that will determine many features of the random walk: recurrence/transience, non-zero limiting speed, limiting distributions and more. In this talk I will prove functional limit laws for one-dimensional excited random walks that are recurrent. For certain values of the parameters in the model the random walks under diffusive scaling converge to a Brownian motion perturbed at its extremum. This was known previously for the case of excited random walks with boundedly many cookies per site, but we are able to generalize this to excited random walks with periodic cookie stacks. In this more general case, it is much less clear why perturbed Brownian motion should be the correct scaling limit. This is joint work with Elena Kosygina.<br />
<br />
<!-- == March 7, TBA == --><br />
<br />
<!-- == March 14, TBA == --><br />
<br />
== March 21, Spring Break, No seminar ==<br />
<br />
== March 28, [https://www.math.wisc.edu/~shamgar/ Shamgar Gurevitch] [https://www.math.wisc.edu/ UW-Madison]==<br />
<br />
Title: '''Harmonic Analysis on GLn over finite fields, and Random Walks'''<br />
<br />
Abstract: There are many formulas that express interesting properties of a group G in terms of sums over its characters. For evaluating or estimating these sums, one of the most salient quantities to understand is the ''character ratio'': <br />
<br />
$$<br />
\text{trace}(\rho(g))/\text{dim}(\rho),<br />
$$<br />
<br />
for an irreducible representation $\rho$ of G and an element g of G. For example, Diaconis and Shahshahani stated a formula of this type for analyzing G-biinvariant random walks on G. It turns out that, for classical groups G over finite fields (which provide most examples of finite simple groups), there is a natural invariant of representations that provides strong information on the character ratio. We call this invariant ''rank''. This talk will discuss the notion of rank for $GL_n$ over finite fields, and apply the results to random walks. This is joint work with Roger Howe (Yale and Texas AM).<br />
<br />
== April 4, [https://www.math.wisc.edu/~pmwood/ Philip Matchett Wood], [http://www.math.wisc.edu/ UW-Madison] ==<br />
<br />
Title: '''Outliers in the spectrum for products of independent random matrices'''<br />
<br />
Abstract: For fixed positive integers m, we consider the product of m independent n by n random matrices with iid entries as in the limit as n tends to infinity. Under suitable assumptions on the entries of each matrix, it is known that the limiting empirical distribution of the eigenvalues is described by the m-th power of the circular law. Moreover, this same limiting distribution continues to hold if each iid random matrix is additively perturbed by a bounded rank deterministic error. However, the bounded rank perturbations may create one or more outlier eigenvalues. We describe the asymptotic location of the outlier eigenvalues, which extends a result of Terence Tao for the case of a single iid matrix. Our methods also allow us to consider several other types of perturbations, including multiplicative perturbations. Joint work with Natalie Coston and Sean O'Rourke.<br />
<br />
== April 11, [https://sites.google.com/site/ebprocaccia/ Eviatar Procaccia], [http://www.math.tamu.edu/index.html Texas A&M] ==<br />
<br />
Stabilization of Diffusion Limited Aggregation in a Wedge. <br />
<br />
Abstract: We prove a discrete Beurling estimate for the harmonic measure in a wedge in $\mathbf{Z}^2$, and use it to show that Diffusion Limited Aggregation (DLA) in a wedge of angle smaller than $\pi/4$ stabilizes. This allows to consider the infinite DLA and questions about the number of arms, growth and dimension. I will present some conjectures and open problems.<br />
<br />
== April 18, [https://services.math.duke.edu/~agazzi/index.html Andrea Agazzi], [https://math.duke.edu/ Duke] ==<br />
<br />
== April 25, [https://www.brown.edu/academics/applied-mathematics/kavita-ramanan Kavita Ramanan], [https://www.brown.edu/academics/applied-mathematics/ Brown] ==<br />
<br />
== April 26, Colloquium, [https://www.brown.edu/academics/applied-mathematics/kavita-ramanan Kavita Ramanan], [https://www.brown.edu/academics/applied-mathematics/ Brown] ==<br />
<br />
<!-- == April 26, TBA == --><br />
<br />
== May 2, TBA ==<br />
<br />
<br />
<!--<br />
==<span style="color:red"> Friday, August 10, 10am, B239 Van Vleck </span> András Mészáros, Central European University, Budapest ==<br />
<br />
<br />
Title: '''The distribution of sandpile groups of random regular graphs'''<br />
<br />
Abstract:<br />
We study the distribution of the sandpile group of random <math>d</math>-regular graphs. For the directed model we prove that it follows the Cohen-Lenstra heuristics, that is, the probability that the <math>p</math>-Sylow subgroup of the sandpile group is a given <math>p</math>-group <math>P</math>, is proportional to <math>|\operatorname{Aut}(P)|^{-1}</math>. For finitely many primes, these events get independent in limit. Similar results hold for undirected random regular graphs, there for odd primes the limiting distributions are the ones given by Clancy, Leake and Payne.<br />
<br />
Our results extends a recent theorem of Huang saying that the adjacency matrices of random <math>d</math>-regular directed graphs are invertible with high probability to the undirected case.<br />
<br />
<br />
==September 20, [http://math.columbia.edu/~hshen/ Hao Shen], [https://www.math.wisc.edu/ UW-Madison] ==<br />
<br />
Title: '''Stochastic quantization of Yang-Mills'''<br />
<br />
Abstract:<br />
"Stochastic quantization” refers to a formulation of quantum field theory as stochastic PDEs. Interesting progress has been made these years in understanding these SPDEs, examples including Phi4 and sine-Gordon. Yang-Mills is a type of quantum field theory which has gauge symmetry, and its stochastic quantization is a Yang-Mills flow perturbed by white noise.<br />
In this talk we start by an Abelian example where we take a symmetry-preserving lattice regularization and study the continuum limit. We will then discuss non-Abelian Yang-Mills theories and introduce a symmetry-breaking smooth regularization and restore the symmetry using a notion of gauge-equivariance. With these results we can construct dynamical Wilson loop and string observables. Based on [S., arXiv:1801.04596] and [Chandra,Hairer,S., work in progress].<br />
<br />
--><br />
<br />
== ==<br />
<br />
[[Past Seminars]]</div>Adminhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia&diff=17257Colloquia2019-04-01T16:05:24Z<p>Admin: /* Spring 2019 */</p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
==Spring 2019==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Jan 25 '''Room 911'''<br />
| [http://www.users.miamioh.edu/randrib/ Beata Randrianantoanina] (Miami University Ohio) WIMAW<br />
|[[#Beata Randrianantoanina (Miami University Ohio) | Some nonlinear problems in the geometry of Banach spaces and their applications ]]<br />
| Tullia Dymarz<br />
|<br />
|-<br />
|Jan 30 '''Wednesday'''<br />
| Talk rescheduled to Feb 15<br />
|<br />
|-<br />
|Jan 31 '''Thursday'''<br />
| Talk rescheduled to Feb 13<br />
|<br />
|-<br />
|Feb 1<br />
| Talk cancelled due to weather<br />
|<br />
| <br />
|<br />
|-<br />
|Feb 5 '''Tuesday, VV 911'''<br />
| [http://www.math.tamu.edu/~alexei.poltoratski/ Alexei Poltoratski] (Texas A&M University)<br />
|[[#Alexei Poltoratski (Texas A&M)| Completeness of exponentials: Beurling-Malliavin and type problems ]]<br />
| Denisov<br />
|<br />
|-<br />
|Feb 6 '''Wednesday, room 911'''<br />
| [https://lc-tsai.github.io/ Li-Cheng Tsai] (Columbia University)<br />
|[[#Li-Cheng Tsai (Columbia University)| When particle systems meet PDEs ]]<br />
| Anderson<br />
|<br />
|-<br />
|Feb 8<br />
| [https://sites.math.northwestern.edu/~anaber/ Aaron Naber] (Northwestern)<br />
|[[#Aaron Naber (Northwestern) | A structure theory for spaces with lower Ricci curvature bounds ]]<br />
| Street<br />
|<br />
|-<br />
|Feb 11 '''Monday'''<br />
| [https://www2.bc.edu/david-treumann/materials.html David Treumann] (Boston College)<br />
|[[#David Treumann (Boston College) | Twisting things in topology and symplectic topology by pth powers ]]<br />
| Caldararu<br />
|<br />
|-<br />
| Feb 13 '''Wednesday'''<br />
| [http://www.math.tamu.edu/~dbaskin/ Dean Baskin] (Texas A&M)<br />
|[[#Dean Baskin (Texas A&M) | Radiation fields for wave equations ]]<br />
| Street<br />
<br />
|-<br />
| Feb 15 <br />
| [https://services.math.duke.edu/~pierce/ Lillian Pierce] (Duke University)<br />
| [[#Lillian Pierce (Duke University) | Short character sums ]]<br />
| Boston and Street<br />
|<br />
|-<br />
|Feb 22<br />
| [https://people.math.osu.edu/cueto.5/ Angelica Cueto] (Ohio State)<br />
|[[#Angelica Cueto (The Ohio State University)| Lines on cubic surfaces in the tropics ]]<br />
| Erman and Corey<br />
|<br />
|-<br />
|March 4 '''Monday'''<br />
| [http://www-users.math.umn.edu/~sverak/ Vladimir Sverak] (Minnesota) <br />
|[[#Vladimir Sverak (Minnesota) | Wasow lecture "PDE aspects of the Navier-Stokes equations and simpler models" ]]<br />
| Kim<br />
|<br />
|-<br />
|March 8<br />
| [https://orion.math.iastate.edu/jmccullo/index.html Jason McCullough] (Iowa State)<br />
|[[#Jason McCullough (Iowa State)| On the degrees and complexity of algebraic varieties ]]<br />
| Erman<br />
|<br />
|-<br />
|March 15<br />
| <s>[http://www.its.caltech.edu/~maksym/ Maksym Radziwill] (Caltech)</s> <b>Talk cancelled</b><br />
|[[#Maksym Radziwill (Caltech) | <s>Recent progress in multiplicative number theory</s> ]]<br />
| Marshall<br />
|<br />
|-<br />
|March 29<br />
| Jennifer Park (OSU)<br />
|[[#Jennifer Park (OSU) | Rational points on varieties ]]<br />
| Marshall<br />
|<br />
|-<br />
|April 5<br />
| Ju-Lee Kim (MIT)<br />
|[[# TBA| TBA ]]<br />
| Gurevich<br />
|<br />
|-<br />
|April 12<br />
| Eviatar Procaccia (TAMU)<br />
|[[#Eviatar Procaccia | Can one hear the shape of a random walk? ]]<br />
| Gurevich<br />
|<br />
|-<br />
|April 19<br />
| [http://www.math.rice.edu/~jkn3/ Jo Nelson] (Rice University)<br />
|[[# TBA| TBA ]]<br />
| Jean-Luc<br />
|<br />
|-<br />
|April 22 '''Monday'''<br />
| [https://justinh.su Justin Hsu] (Madison)<br />
|[[# TBA| TBA ]]<br />
| Lempp<br />
|<br />
|-<br />
|April 26<br />
| [https://www.brown.edu/academics/applied-mathematics/faculty/kavita-ramanan/home Kavita Ramanan] (Brown University)<br />
|[[# TBA| TBA ]]<br />
| WIMAW<br />
|<br />
|-<br />
|May 3<br />
| Tomasz Przebinda (Oklahoma)<br />
|[[# TBA| TBA ]]<br />
| Gurevich<br />
|<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Beata Randrianantoanina (Miami University Ohio)===<br />
<br />
Title: Some nonlinear problems in the geometry of Banach spaces and their applications.<br />
<br />
Abstract: Nonlinear problems in the geometry of Banach spaces have been studied since the inception of the field. In this talk I will outline some of the history, some of modern applications, and some open directions of research. The talk will be accessible to graduate students of any field of mathematics.<br />
<br />
===Lillian Pierce (Duke University)===<br />
<br />
Title: Short character sums <br />
<br />
Abstract: A surprisingly diverse array of problems in analytic number theory have at their heart a problem of bounding (from above) an exponential sum, or its multiplicative cousin, a so-called character sum. For example, both understanding the Riemann zeta function or Dirichlet L-functions inside the critical strip, and also counting solutions to Diophantine equations via the circle method or power sieve methods, involve bounding such sums. In general, the sums of interest fall into one of two main regimes: complete sums or incomplete sums, with this latter regime including in particular “short sums.” Short sums are particularly useful, and particularly resistant to almost all known methods. In this talk, we will see what makes a sum “short,” sketch why it would be incredibly powerful to understand short sums, and discuss a curious proof from the 1950’s which is still the best way we know to bound short sums. We will end by describing new work which extends the ideas of this curious proof to bound short sums in much more general situations.<br />
<br />
===Angelica Cueto (The Ohio State University)===<br />
Title: Lines on cubic surfaces in the tropics<br />
<br />
Abstract: Since the beginning of tropical geometry, a persistent challenge has been to emulate tropical versions of classical results in algebraic geometry. The well-know statement <i>any smooth surface of degree three in P^3 contains exactly 27 lines</i> is known to be false tropically. Work of Vigeland from 2007 provides examples of tropical cubic surfaces with infinitely many lines and gives a classification of tropical lines on general smooth tropical surfaces in TP^3.<br />
<br />
In this talk I will explain how to correct this pathology by viewing the surface as a del Pezzo cubic and considering its embedding in P^44 via its anticanonical bundle. The combinatorics of the root system of type E_6 and a tropical notion of convexity will play a central role in the construction. This is joint work in progress with Anand Deopurkar.<br />
<br />
===David Treumann (Boston College)===<br />
<br />
Title: Twisting things in topology and symplectic topology by pth powers<br />
<br />
Abstract: There's an old and popular analogy between circles and finite fields. I'll describe some constructions you can make in Lagrangian Floer theory and in microlocal sheaf theory by taking this analogy extremely literally, the main ingredient is an "F-field." An F-field on a manifold M is a local system of algebraically closed fields of characteristic p. When M is symplectic, maybe an F-field should remind you of a B-field, it can be used to change the Fukaya category in about the same way. On M = S^1 times R^3, this version of the Fukaya category is related to Deligne-Lusztig theory, and I found something like a cluster structure on the Deligne-Lusztig pairing varieties by studying it. On M = S^1 times S^1, Yanki Lekili and I have found that this version of the Fukaya category is related to the equal-characteristic version of the Fargues-Fontaine curve; the relationship is homological mirror symmetry.<br />
<br />
===Dean Baskin (Texas A&M)===<br />
<br />
Title: Radiation fields for wave equations<br />
<br />
Abstract: Radiation fields are rescaled limits of solutions of wave equations near "null infinity" and capture the radiation pattern seen by a distant observer. They are intimately connected with the Fourier and Radon transforms and with scattering theory. In this talk, I will define and discuss radiation fields in a few contexts, with an emphasis on spacetimes that look flat near infinity. The main result is a connection between the asymptotic behavior of the radiation field and a family of quantum objects on an associated asymptotically hyperbolic space.<br />
<br />
===Jianfeng Lu (Duke University)===<br />
<br />
Title: Density fitting: Analysis, algorithm and applications<br />
<br />
Abstract: Density fitting considers the low-rank approximation of pair products of eigenfunctions of Hamiltonian operators. It is a very useful tool with many applications in electronic structure theory. In this talk, we will discuss estimates of upper bound of the numerical rank of the pair products of eigenfunctions. We will also introduce the interpolative separable density fitting (ISDF) algorithm, which reduces the computational scaling of the low-rank approximation and can be used for efficient algorithms for electronic structure calculations. Based on joint works with Chris Sogge, Stefan Steinerberger, Kyle Thicke, and Lexing Ying.<br />
<br />
===Alexei Poltoratski (Texas A&M)===<br />
<br />
Title: Completeness of exponentials: Beurling-Malliavin and type problems<br />
<br />
Abstract: This talk is devoted to two old problems of harmonic analysis mentioned in the title. Both<br />
problems ask when a family of complex exponentials is complete (spans) an L^2-space. The Beruling-Malliavin<br />
problem was solved in the early 1960s and I will present its classical solution along with modern generalizations<br />
and applications. I will then discuss history and recent progress in the type problem, which stood open for<br />
more than 70 years.<br />
<br />
===Li-Cheng Tsai (Columbia University)===<br />
<br />
Title: When particle systems meet PDEs<br />
<br />
Interacting particle systems are models that involve many randomly evolving agents (i.e., particles). These systems are widely used in describing real-world phenomena. In this talk we will walk through three facets of interacting particle systems, namely the law of large numbers, random fluctuations, and large deviations. Within each facet, I will explain how Partial Differential Equations (PDEs) play a role in understanding the systems.<br />
<br />
===Aaron Naber (Northwestern)===<br />
<br />
Title: A structure theory for spaces with lower Ricci curvature bounds.<br />
<br />
Abstract: One should view manifolds (M^n,g) with lower Ricci curvature bounds as being those manifolds with a well behaved analysis, a point which can be rigorously stated. It thus becomes a natural question, how well behaved or badly behaved can such spaces be? This is a nonlinear analogue to asking how degenerate can a subharmonic or plurisubharmonic function look like. In this talk we give an essentially sharp answer to this question. The talk will require little background, and our time will be spent on understanding the basic statements and examples. The work discussed is joint with Cheeger, Jiang and with Li.<br />
<br />
<br />
===Vladimir Sverak (Minnesota)===<br />
<br />
Title: PDE aspects of the Navier-Stokes equations and simpler models<br />
<br />
Abstract: Does the Navier-Stokes equation give a reasonably complete description of fluid motion? There seems to be no empirical evidence which would suggest a negative answer (in regimes which are not extreme), but from the purely mathematical point of view, the answer may not be so clear. In the lecture, I will discuss some of the possible scenarios and open problems for both the full equations and simplified models.<br />
<br />
<br />
===Jason McCullough (Iowa State)===<br />
<br />
Title: On the degrees and complexity of algebraic varieties<br />
<br />
Abstract: Given a system of polynomial equations in several variables, there are several natural questions regarding its associated solution set (algebraic variety): What is its dimension? Is it smooth or are there singularities? How is it embedded in affine/projective space? Free resolutions encode answers to all of these questions and are computable with modern computer algebra programs. This begs the question: can one bound the computational complexity of a variety in terms of readily available data? I will discuss two recently solved conjectures of Stillman and Eisenbud-Goto, how they relate to each other, and what they say about the complexity of algebraic varieties.<br />
<br />
===Maksym Radziwill (Caltech)===<br />
<br />
Title: Recent progress in multiplicative number theory<br />
<br />
Abstract: Multiplicative number theory aims to understand the ways in which integers factorize, and the distribution of integers with special multiplicative properties (such as primes). It is a central area of analytic number theory with various connections to L-functions, harmonic analysis, combinatorics, probability etc. At the core of the subject lie difficult questions such as the Riemann Hypothesis, and they set a benchmark for its accomplishments.<br />
An outstanding challenge in this field is to understand the multiplicative properties of integers linked by additive conditions, for instance n and n+ 1. A central conjecture making this precise is the Chowla-Elliott conjecture on correlations of multiplicative functions evaluated at consecutive integers. Until recently this conjecture appeared completely out of reach and was thought to be at least as difficult as showing the existence of infinitely many twin primes. These are also the kind of questions that lie beyond the capability of the Riemann Hypothesis. However recently the landscape of multiplicative number theory has been changing and we are no longer so certain about the limitations of our (new) tools. I will discuss the recent progress on these questions.<br />
<br />
===Jennifer Park (OSU)===<br />
<br />
Title: Rational points on varieties<br />
<br />
Abstract: The question of finding rational solutions to systems of polynomial equations has been investigated at least since the days of Pythagoras, but it is still not completely resolved (and in fact, it has been proven that there will never be an algorithm that answers this question!) Nonetheless, we will discuss various techniques that could answer this question in certain cases, and we will outline some conjectures related to this problem as well.<br />
<br />
<br />
===Eviatar Procaccia===<br />
Title: Can one hear the shape of a random walk?<br />
<br />
Abstract: We consider a Gibbs distribution over random walk paths on the square lattice, proportional to a random weight of the path’s boundary . We show that in the zero temperature limit, the paths condensate around an asymptotic shape. This limit shape is characterized as the minimizer of the functional, mapping open connected subsets of the plane to the sum of their principle eigenvalue and perimeter (with respect to the first passage percolation norm). A prime novel feature of this limit shape is that it is not in the class of Wulff shapes.<br />
Joint work with Marek Biskup (UCLA)<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank]]<br />
<br />
[[Colloquia/Fall2018|Fall 2018]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Adminhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia&diff=17256Colloquia2019-04-01T16:04:46Z<p>Admin: /* Abstracts */</p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
==Spring 2019==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Jan 25 '''Room 911'''<br />
| [http://www.users.miamioh.edu/randrib/ Beata Randrianantoanina] (Miami University Ohio) WIMAW<br />
|[[#Beata Randrianantoanina (Miami University Ohio) | Some nonlinear problems in the geometry of Banach spaces and their applications ]]<br />
| Tullia Dymarz<br />
|<br />
|-<br />
|Jan 30 '''Wednesday'''<br />
| Talk rescheduled to Feb 15<br />
|<br />
|-<br />
|Jan 31 '''Thursday'''<br />
| Talk rescheduled to Feb 13<br />
|<br />
|-<br />
|Feb 1<br />
| Talk cancelled due to weather<br />
|<br />
| <br />
|<br />
|-<br />
|Feb 5 '''Tuesday, VV 911'''<br />
| [http://www.math.tamu.edu/~alexei.poltoratski/ Alexei Poltoratski] (Texas A&M University)<br />
|[[#Alexei Poltoratski (Texas A&M)| Completeness of exponentials: Beurling-Malliavin and type problems ]]<br />
| Denisov<br />
|<br />
|-<br />
|Feb 6 '''Wednesday, room 911'''<br />
| [https://lc-tsai.github.io/ Li-Cheng Tsai] (Columbia University)<br />
|[[#Li-Cheng Tsai (Columbia University)| When particle systems meet PDEs ]]<br />
| Anderson<br />
|<br />
|-<br />
|Feb 8<br />
| [https://sites.math.northwestern.edu/~anaber/ Aaron Naber] (Northwestern)<br />
|[[#Aaron Naber (Northwestern) | A structure theory for spaces with lower Ricci curvature bounds ]]<br />
| Street<br />
|<br />
|-<br />
|Feb 11 '''Monday'''<br />
| [https://www2.bc.edu/david-treumann/materials.html David Treumann] (Boston College)<br />
|[[#David Treumann (Boston College) | Twisting things in topology and symplectic topology by pth powers ]]<br />
| Caldararu<br />
|<br />
|-<br />
| Feb 13 '''Wednesday'''<br />
| [http://www.math.tamu.edu/~dbaskin/ Dean Baskin] (Texas A&M)<br />
|[[#Dean Baskin (Texas A&M) | Radiation fields for wave equations ]]<br />
| Street<br />
<br />
|-<br />
| Feb 15 <br />
| [https://services.math.duke.edu/~pierce/ Lillian Pierce] (Duke University)<br />
| [[#Lillian Pierce (Duke University) | Short character sums ]]<br />
| Boston and Street<br />
|<br />
|-<br />
|Feb 22<br />
| [https://people.math.osu.edu/cueto.5/ Angelica Cueto] (Ohio State)<br />
|[[#Angelica Cueto (The Ohio State University)| Lines on cubic surfaces in the tropics ]]<br />
| Erman and Corey<br />
|<br />
|-<br />
|March 4 '''Monday'''<br />
| [http://www-users.math.umn.edu/~sverak/ Vladimir Sverak] (Minnesota) <br />
|[[#Vladimir Sverak (Minnesota) | Wasow lecture "PDE aspects of the Navier-Stokes equations and simpler models" ]]<br />
| Kim<br />
|<br />
|-<br />
|March 8<br />
| [https://orion.math.iastate.edu/jmccullo/index.html Jason McCullough] (Iowa State)<br />
|[[#Jason McCullough (Iowa State)| On the degrees and complexity of algebraic varieties ]]<br />
| Erman<br />
|<br />
|-<br />
|March 15<br />
| <s>[http://www.its.caltech.edu/~maksym/ Maksym Radziwill] (Caltech)</s> <b>Talk cancelled</b><br />
|[[#Maksym Radziwill (Caltech) | <s>Recent progress in multiplicative number theory</s> ]]<br />
| Marshall<br />
|<br />
|-<br />
|March 29<br />
| Jennifer Park (OSU)<br />
|[[#Jennifer Park (OSU) | Rational points on varieties ]]<br />
| Marshall<br />
|<br />
|-<br />
|April 5<br />
| Ju-Lee Kim (MIT)<br />
|[[# TBA| TBA ]]<br />
| Gurevich<br />
|<br />
|-<br />
|April 12<br />
| Eviatar Procaccia (TAMU)<br />
|[[# TBA| Can one hear the shape of a random walk? ]]<br />
| Gurevich<br />
|<br />
|-<br />
|April 19<br />
| [http://www.math.rice.edu/~jkn3/ Jo Nelson] (Rice University)<br />
|[[# TBA| TBA ]]<br />
| Jean-Luc<br />
|<br />
|-<br />
|April 22 '''Monday'''<br />
| [https://justinh.su Justin Hsu] (Madison)<br />
|[[# TBA| TBA ]]<br />
| Lempp<br />
|<br />
|-<br />
|April 26<br />
| [https://www.brown.edu/academics/applied-mathematics/faculty/kavita-ramanan/home Kavita Ramanan] (Brown University)<br />
|[[# TBA| TBA ]]<br />
| WIMAW<br />
|<br />
|-<br />
|May 3<br />
| Tomasz Przebinda (Oklahoma)<br />
|[[# TBA| TBA ]]<br />
| Gurevich<br />
|<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Beata Randrianantoanina (Miami University Ohio)===<br />
<br />
Title: Some nonlinear problems in the geometry of Banach spaces and their applications.<br />
<br />
Abstract: Nonlinear problems in the geometry of Banach spaces have been studied since the inception of the field. In this talk I will outline some of the history, some of modern applications, and some open directions of research. The talk will be accessible to graduate students of any field of mathematics.<br />
<br />
===Lillian Pierce (Duke University)===<br />
<br />
Title: Short character sums <br />
<br />
Abstract: A surprisingly diverse array of problems in analytic number theory have at their heart a problem of bounding (from above) an exponential sum, or its multiplicative cousin, a so-called character sum. For example, both understanding the Riemann zeta function or Dirichlet L-functions inside the critical strip, and also counting solutions to Diophantine equations via the circle method or power sieve methods, involve bounding such sums. In general, the sums of interest fall into one of two main regimes: complete sums or incomplete sums, with this latter regime including in particular “short sums.” Short sums are particularly useful, and particularly resistant to almost all known methods. In this talk, we will see what makes a sum “short,” sketch why it would be incredibly powerful to understand short sums, and discuss a curious proof from the 1950’s which is still the best way we know to bound short sums. We will end by describing new work which extends the ideas of this curious proof to bound short sums in much more general situations.<br />
<br />
===Angelica Cueto (The Ohio State University)===<br />
Title: Lines on cubic surfaces in the tropics<br />
<br />
Abstract: Since the beginning of tropical geometry, a persistent challenge has been to emulate tropical versions of classical results in algebraic geometry. The well-know statement <i>any smooth surface of degree three in P^3 contains exactly 27 lines</i> is known to be false tropically. Work of Vigeland from 2007 provides examples of tropical cubic surfaces with infinitely many lines and gives a classification of tropical lines on general smooth tropical surfaces in TP^3.<br />
<br />
In this talk I will explain how to correct this pathology by viewing the surface as a del Pezzo cubic and considering its embedding in P^44 via its anticanonical bundle. The combinatorics of the root system of type E_6 and a tropical notion of convexity will play a central role in the construction. This is joint work in progress with Anand Deopurkar.<br />
<br />
===David Treumann (Boston College)===<br />
<br />
Title: Twisting things in topology and symplectic topology by pth powers<br />
<br />
Abstract: There's an old and popular analogy between circles and finite fields. I'll describe some constructions you can make in Lagrangian Floer theory and in microlocal sheaf theory by taking this analogy extremely literally, the main ingredient is an "F-field." An F-field on a manifold M is a local system of algebraically closed fields of characteristic p. When M is symplectic, maybe an F-field should remind you of a B-field, it can be used to change the Fukaya category in about the same way. On M = S^1 times R^3, this version of the Fukaya category is related to Deligne-Lusztig theory, and I found something like a cluster structure on the Deligne-Lusztig pairing varieties by studying it. On M = S^1 times S^1, Yanki Lekili and I have found that this version of the Fukaya category is related to the equal-characteristic version of the Fargues-Fontaine curve; the relationship is homological mirror symmetry.<br />
<br />
===Dean Baskin (Texas A&M)===<br />
<br />
Title: Radiation fields for wave equations<br />
<br />
Abstract: Radiation fields are rescaled limits of solutions of wave equations near "null infinity" and capture the radiation pattern seen by a distant observer. They are intimately connected with the Fourier and Radon transforms and with scattering theory. In this talk, I will define and discuss radiation fields in a few contexts, with an emphasis on spacetimes that look flat near infinity. The main result is a connection between the asymptotic behavior of the radiation field and a family of quantum objects on an associated asymptotically hyperbolic space.<br />
<br />
===Jianfeng Lu (Duke University)===<br />
<br />
Title: Density fitting: Analysis, algorithm and applications<br />
<br />
Abstract: Density fitting considers the low-rank approximation of pair products of eigenfunctions of Hamiltonian operators. It is a very useful tool with many applications in electronic structure theory. In this talk, we will discuss estimates of upper bound of the numerical rank of the pair products of eigenfunctions. We will also introduce the interpolative separable density fitting (ISDF) algorithm, which reduces the computational scaling of the low-rank approximation and can be used for efficient algorithms for electronic structure calculations. Based on joint works with Chris Sogge, Stefan Steinerberger, Kyle Thicke, and Lexing Ying.<br />
<br />
===Alexei Poltoratski (Texas A&M)===<br />
<br />
Title: Completeness of exponentials: Beurling-Malliavin and type problems<br />
<br />
Abstract: This talk is devoted to two old problems of harmonic analysis mentioned in the title. Both<br />
problems ask when a family of complex exponentials is complete (spans) an L^2-space. The Beruling-Malliavin<br />
problem was solved in the early 1960s and I will present its classical solution along with modern generalizations<br />
and applications. I will then discuss history and recent progress in the type problem, which stood open for<br />
more than 70 years.<br />
<br />
===Li-Cheng Tsai (Columbia University)===<br />
<br />
Title: When particle systems meet PDEs<br />
<br />
Interacting particle systems are models that involve many randomly evolving agents (i.e., particles). These systems are widely used in describing real-world phenomena. In this talk we will walk through three facets of interacting particle systems, namely the law of large numbers, random fluctuations, and large deviations. Within each facet, I will explain how Partial Differential Equations (PDEs) play a role in understanding the systems.<br />
<br />
===Aaron Naber (Northwestern)===<br />
<br />
Title: A structure theory for spaces with lower Ricci curvature bounds.<br />
<br />
Abstract: One should view manifolds (M^n,g) with lower Ricci curvature bounds as being those manifolds with a well behaved analysis, a point which can be rigorously stated. It thus becomes a natural question, how well behaved or badly behaved can such spaces be? This is a nonlinear analogue to asking how degenerate can a subharmonic or plurisubharmonic function look like. In this talk we give an essentially sharp answer to this question. The talk will require little background, and our time will be spent on understanding the basic statements and examples. The work discussed is joint with Cheeger, Jiang and with Li.<br />
<br />
<br />
===Vladimir Sverak (Minnesota)===<br />
<br />
Title: PDE aspects of the Navier-Stokes equations and simpler models<br />
<br />
Abstract: Does the Navier-Stokes equation give a reasonably complete description of fluid motion? There seems to be no empirical evidence which would suggest a negative answer (in regimes which are not extreme), but from the purely mathematical point of view, the answer may not be so clear. In the lecture, I will discuss some of the possible scenarios and open problems for both the full equations and simplified models.<br />
<br />
<br />
===Jason McCullough (Iowa State)===<br />
<br />
Title: On the degrees and complexity of algebraic varieties<br />
<br />
Abstract: Given a system of polynomial equations in several variables, there are several natural questions regarding its associated solution set (algebraic variety): What is its dimension? Is it smooth or are there singularities? How is it embedded in affine/projective space? Free resolutions encode answers to all of these questions and are computable with modern computer algebra programs. This begs the question: can one bound the computational complexity of a variety in terms of readily available data? I will discuss two recently solved conjectures of Stillman and Eisenbud-Goto, how they relate to each other, and what they say about the complexity of algebraic varieties.<br />
<br />
===Maksym Radziwill (Caltech)===<br />
<br />
Title: Recent progress in multiplicative number theory<br />
<br />
Abstract: Multiplicative number theory aims to understand the ways in which integers factorize, and the distribution of integers with special multiplicative properties (such as primes). It is a central area of analytic number theory with various connections to L-functions, harmonic analysis, combinatorics, probability etc. At the core of the subject lie difficult questions such as the Riemann Hypothesis, and they set a benchmark for its accomplishments.<br />
An outstanding challenge in this field is to understand the multiplicative properties of integers linked by additive conditions, for instance n and n+ 1. A central conjecture making this precise is the Chowla-Elliott conjecture on correlations of multiplicative functions evaluated at consecutive integers. Until recently this conjecture appeared completely out of reach and was thought to be at least as difficult as showing the existence of infinitely many twin primes. These are also the kind of questions that lie beyond the capability of the Riemann Hypothesis. However recently the landscape of multiplicative number theory has been changing and we are no longer so certain about the limitations of our (new) tools. I will discuss the recent progress on these questions.<br />
<br />
===Jennifer Park (OSU)===<br />
<br />
Title: Rational points on varieties<br />
<br />
Abstract: The question of finding rational solutions to systems of polynomial equations has been investigated at least since the days of Pythagoras, but it is still not completely resolved (and in fact, it has been proven that there will never be an algorithm that answers this question!) Nonetheless, we will discuss various techniques that could answer this question in certain cases, and we will outline some conjectures related to this problem as well.<br />
<br />
<br />
===Eviatar Procaccia===<br />
Title: Can one hear the shape of a random walk?<br />
<br />
Abstract: We consider a Gibbs distribution over random walk paths on the square lattice, proportional to a random weight of the path’s boundary . We show that in the zero temperature limit, the paths condensate around an asymptotic shape. This limit shape is characterized as the minimizer of the functional, mapping open connected subsets of the plane to the sum of their principle eigenvalue and perimeter (with respect to the first passage percolation norm). A prime novel feature of this limit shape is that it is not in the class of Wulff shapes.<br />
Joint work with Marek Biskup (UCLA)<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank]]<br />
<br />
[[Colloquia/Fall2018|Fall 2018]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Adminhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia&diff=17255Colloquia2019-04-01T16:03:13Z<p>Admin: </p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
==Spring 2019==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Jan 25 '''Room 911'''<br />
| [http://www.users.miamioh.edu/randrib/ Beata Randrianantoanina] (Miami University Ohio) WIMAW<br />
|[[#Beata Randrianantoanina (Miami University Ohio) | Some nonlinear problems in the geometry of Banach spaces and their applications ]]<br />
| Tullia Dymarz<br />
|<br />
|-<br />
|Jan 30 '''Wednesday'''<br />
| Talk rescheduled to Feb 15<br />
|<br />
|-<br />
|Jan 31 '''Thursday'''<br />
| Talk rescheduled to Feb 13<br />
|<br />
|-<br />
|Feb 1<br />
| Talk cancelled due to weather<br />
|<br />
| <br />
|<br />
|-<br />
|Feb 5 '''Tuesday, VV 911'''<br />
| [http://www.math.tamu.edu/~alexei.poltoratski/ Alexei Poltoratski] (Texas A&M University)<br />
|[[#Alexei Poltoratski (Texas A&M)| Completeness of exponentials: Beurling-Malliavin and type problems ]]<br />
| Denisov<br />
|<br />
|-<br />
|Feb 6 '''Wednesday, room 911'''<br />
| [https://lc-tsai.github.io/ Li-Cheng Tsai] (Columbia University)<br />
|[[#Li-Cheng Tsai (Columbia University)| When particle systems meet PDEs ]]<br />
| Anderson<br />
|<br />
|-<br />
|Feb 8<br />
| [https://sites.math.northwestern.edu/~anaber/ Aaron Naber] (Northwestern)<br />
|[[#Aaron Naber (Northwestern) | A structure theory for spaces with lower Ricci curvature bounds ]]<br />
| Street<br />
|<br />
|-<br />
|Feb 11 '''Monday'''<br />
| [https://www2.bc.edu/david-treumann/materials.html David Treumann] (Boston College)<br />
|[[#David Treumann (Boston College) | Twisting things in topology and symplectic topology by pth powers ]]<br />
| Caldararu<br />
|<br />
|-<br />
| Feb 13 '''Wednesday'''<br />
| [http://www.math.tamu.edu/~dbaskin/ Dean Baskin] (Texas A&M)<br />
|[[#Dean Baskin (Texas A&M) | Radiation fields for wave equations ]]<br />
| Street<br />
<br />
|-<br />
| Feb 15 <br />
| [https://services.math.duke.edu/~pierce/ Lillian Pierce] (Duke University)<br />
| [[#Lillian Pierce (Duke University) | Short character sums ]]<br />
| Boston and Street<br />
|<br />
|-<br />
|Feb 22<br />
| [https://people.math.osu.edu/cueto.5/ Angelica Cueto] (Ohio State)<br />
|[[#Angelica Cueto (The Ohio State University)| Lines on cubic surfaces in the tropics ]]<br />
| Erman and Corey<br />
|<br />
|-<br />
|March 4 '''Monday'''<br />
| [http://www-users.math.umn.edu/~sverak/ Vladimir Sverak] (Minnesota) <br />
|[[#Vladimir Sverak (Minnesota) | Wasow lecture "PDE aspects of the Navier-Stokes equations and simpler models" ]]<br />
| Kim<br />
|<br />
|-<br />
|March 8<br />
| [https://orion.math.iastate.edu/jmccullo/index.html Jason McCullough] (Iowa State)<br />
|[[#Jason McCullough (Iowa State)| On the degrees and complexity of algebraic varieties ]]<br />
| Erman<br />
|<br />
|-<br />
|March 15<br />
| <s>[http://www.its.caltech.edu/~maksym/ Maksym Radziwill] (Caltech)</s> <b>Talk cancelled</b><br />
|[[#Maksym Radziwill (Caltech) | <s>Recent progress in multiplicative number theory</s> ]]<br />
| Marshall<br />
|<br />
|-<br />
|March 29<br />
| Jennifer Park (OSU)<br />
|[[#Jennifer Park (OSU) | Rational points on varieties ]]<br />
| Marshall<br />
|<br />
|-<br />
|April 5<br />
| Ju-Lee Kim (MIT)<br />
|[[# TBA| TBA ]]<br />
| Gurevich<br />
|<br />
|-<br />
|April 12<br />
| Eviatar Procaccia (TAMU)<br />
|[[# TBA| Can one hear the shape of a random walk? ]]<br />
| Gurevich<br />
|<br />
|-<br />
|April 19<br />
| [http://www.math.rice.edu/~jkn3/ Jo Nelson] (Rice University)<br />
|[[# TBA| TBA ]]<br />
| Jean-Luc<br />
|<br />
|-<br />
|April 22 '''Monday'''<br />
| [https://justinh.su Justin Hsu] (Madison)<br />
|[[# TBA| TBA ]]<br />
| Lempp<br />
|<br />
|-<br />
|April 26<br />
| [https://www.brown.edu/academics/applied-mathematics/faculty/kavita-ramanan/home Kavita Ramanan] (Brown University)<br />
|[[# TBA| TBA ]]<br />
| WIMAW<br />
|<br />
|-<br />
|May 3<br />
| Tomasz Przebinda (Oklahoma)<br />
|[[# TBA| TBA ]]<br />
| Gurevich<br />
|<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Beata Randrianantoanina (Miami University Ohio)===<br />
<br />
Title: Some nonlinear problems in the geometry of Banach spaces and their applications.<br />
<br />
Abstract: Nonlinear problems in the geometry of Banach spaces have been studied since the inception of the field. In this talk I will outline some of the history, some of modern applications, and some open directions of research. The talk will be accessible to graduate students of any field of mathematics.<br />
<br />
===Lillian Pierce (Duke University)===<br />
<br />
Title: Short character sums <br />
<br />
Abstract: A surprisingly diverse array of problems in analytic number theory have at their heart a problem of bounding (from above) an exponential sum, or its multiplicative cousin, a so-called character sum. For example, both understanding the Riemann zeta function or Dirichlet L-functions inside the critical strip, and also counting solutions to Diophantine equations via the circle method or power sieve methods, involve bounding such sums. In general, the sums of interest fall into one of two main regimes: complete sums or incomplete sums, with this latter regime including in particular “short sums.” Short sums are particularly useful, and particularly resistant to almost all known methods. In this talk, we will see what makes a sum “short,” sketch why it would be incredibly powerful to understand short sums, and discuss a curious proof from the 1950’s which is still the best way we know to bound short sums. We will end by describing new work which extends the ideas of this curious proof to bound short sums in much more general situations.<br />
<br />
===Angelica Cueto (The Ohio State University)===<br />
Title: Lines on cubic surfaces in the tropics<br />
<br />
Abstract: Since the beginning of tropical geometry, a persistent challenge has been to emulate tropical versions of classical results in algebraic geometry. The well-know statement <i>any smooth surface of degree three in P^3 contains exactly 27 lines</i> is known to be false tropically. Work of Vigeland from 2007 provides examples of tropical cubic surfaces with infinitely many lines and gives a classification of tropical lines on general smooth tropical surfaces in TP^3.<br />
<br />
In this talk I will explain how to correct this pathology by viewing the surface as a del Pezzo cubic and considering its embedding in P^44 via its anticanonical bundle. The combinatorics of the root system of type E_6 and a tropical notion of convexity will play a central role in the construction. This is joint work in progress with Anand Deopurkar.<br />
<br />
===David Treumann (Boston College)===<br />
<br />
Title: Twisting things in topology and symplectic topology by pth powers<br />
<br />
Abstract: There's an old and popular analogy between circles and finite fields. I'll describe some constructions you can make in Lagrangian Floer theory and in microlocal sheaf theory by taking this analogy extremely literally, the main ingredient is an "F-field." An F-field on a manifold M is a local system of algebraically closed fields of characteristic p. When M is symplectic, maybe an F-field should remind you of a B-field, it can be used to change the Fukaya category in about the same way. On M = S^1 times R^3, this version of the Fukaya category is related to Deligne-Lusztig theory, and I found something like a cluster structure on the Deligne-Lusztig pairing varieties by studying it. On M = S^1 times S^1, Yanki Lekili and I have found that this version of the Fukaya category is related to the equal-characteristic version of the Fargues-Fontaine curve; the relationship is homological mirror symmetry.<br />
<br />
===Dean Baskin (Texas A&M)===<br />
<br />
Title: Radiation fields for wave equations<br />
<br />
Abstract: Radiation fields are rescaled limits of solutions of wave equations near "null infinity" and capture the radiation pattern seen by a distant observer. They are intimately connected with the Fourier and Radon transforms and with scattering theory. In this talk, I will define and discuss radiation fields in a few contexts, with an emphasis on spacetimes that look flat near infinity. The main result is a connection between the asymptotic behavior of the radiation field and a family of quantum objects on an associated asymptotically hyperbolic space.<br />
<br />
===Jianfeng Lu (Duke University)===<br />
<br />
Title: Density fitting: Analysis, algorithm and applications<br />
<br />
Abstract: Density fitting considers the low-rank approximation of pair products of eigenfunctions of Hamiltonian operators. It is a very useful tool with many applications in electronic structure theory. In this talk, we will discuss estimates of upper bound of the numerical rank of the pair products of eigenfunctions. We will also introduce the interpolative separable density fitting (ISDF) algorithm, which reduces the computational scaling of the low-rank approximation and can be used for efficient algorithms for electronic structure calculations. Based on joint works with Chris Sogge, Stefan Steinerberger, Kyle Thicke, and Lexing Ying.<br />
<br />
===Alexei Poltoratski (Texas A&M)===<br />
<br />
Title: Completeness of exponentials: Beurling-Malliavin and type problems<br />
<br />
Abstract: This talk is devoted to two old problems of harmonic analysis mentioned in the title. Both<br />
problems ask when a family of complex exponentials is complete (spans) an L^2-space. The Beruling-Malliavin<br />
problem was solved in the early 1960s and I will present its classical solution along with modern generalizations<br />
and applications. I will then discuss history and recent progress in the type problem, which stood open for<br />
more than 70 years.<br />
<br />
===Li-Cheng Tsai (Columbia University)===<br />
<br />
Title: When particle systems meet PDEs<br />
<br />
Interacting particle systems are models that involve many randomly evolving agents (i.e., particles). These systems are widely used in describing real-world phenomena. In this talk we will walk through three facets of interacting particle systems, namely the law of large numbers, random fluctuations, and large deviations. Within each facet, I will explain how Partial Differential Equations (PDEs) play a role in understanding the systems.<br />
<br />
===Aaron Naber (Northwestern)===<br />
<br />
Title: A structure theory for spaces with lower Ricci curvature bounds.<br />
<br />
Abstract: One should view manifolds (M^n,g) with lower Ricci curvature bounds as being those manifolds with a well behaved analysis, a point which can be rigorously stated. It thus becomes a natural question, how well behaved or badly behaved can such spaces be? This is a nonlinear analogue to asking how degenerate can a subharmonic or plurisubharmonic function look like. In this talk we give an essentially sharp answer to this question. The talk will require little background, and our time will be spent on understanding the basic statements and examples. The work discussed is joint with Cheeger, Jiang and with Li.<br />
<br />
<br />
===Vladimir Sverak (Minnesota)===<br />
<br />
Title: PDE aspects of the Navier-Stokes equations and simpler models<br />
<br />
Abstract: Does the Navier-Stokes equation give a reasonably complete description of fluid motion? There seems to be no empirical evidence which would suggest a negative answer (in regimes which are not extreme), but from the purely mathematical point of view, the answer may not be so clear. In the lecture, I will discuss some of the possible scenarios and open problems for both the full equations and simplified models.<br />
<br />
<br />
===Jason McCullough (Iowa State)===<br />
<br />
Title: On the degrees and complexity of algebraic varieties<br />
<br />
Abstract: Given a system of polynomial equations in several variables, there are several natural questions regarding its associated solution set (algebraic variety): What is its dimension? Is it smooth or are there singularities? How is it embedded in affine/projective space? Free resolutions encode answers to all of these questions and are computable with modern computer algebra programs. This begs the question: can one bound the computational complexity of a variety in terms of readily available data? I will discuss two recently solved conjectures of Stillman and Eisenbud-Goto, how they relate to each other, and what they say about the complexity of algebraic varieties.<br />
<br />
===Maksym Radziwill (Caltech)===<br />
<br />
Title: Recent progress in multiplicative number theory<br />
<br />
Abstract: Multiplicative number theory aims to understand the ways in which integers factorize, and the distribution of integers with special multiplicative properties (such as primes). It is a central area of analytic number theory with various connections to L-functions, harmonic analysis, combinatorics, probability etc. At the core of the subject lie difficult questions such as the Riemann Hypothesis, and they set a benchmark for its accomplishments.<br />
An outstanding challenge in this field is to understand the multiplicative properties of integers linked by additive conditions, for instance n and n+ 1. A central conjecture making this precise is the Chowla-Elliott conjecture on correlations of multiplicative functions evaluated at consecutive integers. Until recently this conjecture appeared completely out of reach and was thought to be at least as difficult as showing the existence of infinitely many twin primes. These are also the kind of questions that lie beyond the capability of the Riemann Hypothesis. However recently the landscape of multiplicative number theory has been changing and we are no longer so certain about the limitations of our (new) tools. I will discuss the recent progress on these questions.<br />
<br />
===Jennifer Park (OSU)===<br />
<br />
Title: Rational points on varieties<br />
<br />
Abstract: The question of finding rational solutions to systems of polynomial equations has been investigated at least since the days of Pythagoras, but it is still not completely resolved (and in fact, it has been proven that there will never be an algorithm that answers this question!) Nonetheless, we will discuss various techniques that could answer this question in certain cases, and we will outline some conjectures related to this problem as well.<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank]]<br />
<br />
[[Colloquia/Fall2018|Fall 2018]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Adminhttps://www.math.wisc.edu/wiki/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Fall_2018&diff=16286Algebra and Algebraic Geometry Seminar Fall 20182018-10-26T19:11:38Z<p>Admin: /* Fall 2018 Schedule */</p>
<hr />
<div>The seminar meets on Fridays at 2:25 pm in room B235.<br />
<br />
Here is the schedule for [[Algebra and Algebraic Geometry Seminar Spring 2018 | the previous semester]], [[Algebra and Algebraic Geometry Seminar Spring 2019 | the next semester]], and for [[Algebra and Algebraic Geometry Seminar | this semester]].<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
<br />
<br />
*Please join the [https://admin.lists.wisc.edu/index.php?p=11&l=ags AGS Mailing List] to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== Fall 2018 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s) <br />
<br />
|-<br />
|September 7<br />
|Daniel Erman<br />
|Big Polynomial Rings<br />
|Local<br />
|-<br />
|September 14<br />
|Akhil Mathew (U Chicago)<br />
|Kaledin's noncommutative degeneration theorem and topological Hochschild homology<br />
|Andrei<br />
|-<br />
|September 21<br />
|Andrei Caldararu<br />
|Categorical Gromov-Witten invariants beyond genus 1<br />
|Local<br />
|-<br />
|September 28<br />
|Mark Walker (Nebraska)<br />
|Conjecture D for matrix factorizations<br />
|Michael and Daniel<br />
|-<br />
|October 5<br />
|-<br />
|-<br />
|-<br />
|-<br />
|October 12<br />
|Jose Rodriguez (Wisconsin)<br />
|TBD<br />
|Local<br />
|-<br />
|October 19<br />
|Oleksandr Tsymbaliuk (Yale)<br />
|Modified quantum difference Toda systems<br />
|Paul Terwilliger<br />
|-<br />
|October 26<br />
|[https://juliettebruce.github.io Juliette Bruce]<br />
|Covering Abelian Varieties and Effective Bertini<br />
|Local<br />
|-<br />
|November 2<br />
|[http://sites.nd.edu/b-taji/ Behrouz Taji] (Notre Dame)<br />
|Remarks on the Kodaira dimension of base spaces of families of manifolds<br />
|Botong Wang<br />
|-<br />
|November 9<br />
|[http://www-personal.umich.edu/~rohitna/ Rohit Nagpal (Michigan)]<br />
|TBD<br />
|John WG<br />
|-<br />
|November 16<br />
|Wanlin Li<br />
|TBD<br />
|Local<br />
|-<br />
|November 23<br />
|Thanksgiving<br />
|No Seminar<br />
|<br />
|-<br />
|November 30<br />
|John Wiltshire-Gordon<br />
|TBD<br />
|Local<br />
|-<br />
|December 7<br />
|Michael Brown<br />
|TBD<br />
|Local<br />
|-<br />
|December 14<br />
|TBD (this date is now open again!)<br />
|TBD<br />
|<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Akhil Mathew===<br />
<br />
'''Title: Kaledin's noncommutative degeneration theorem and topological Hochschild homology'''<br />
<br />
For a smooth proper variety over a field of characteristic<br />
zero, the Hodge-to-de Rham spectral sequence (relating the cohomology<br />
of differential forms to de Rham cohomology) is well-known to<br />
degenerate, via Hodge theory. A "noncommutative" version of this<br />
theorem has been proved by Kaledin for smooth proper dg categories<br />
over a field of characteristic zero, based on the technique of<br />
reduction mod p. I will describe a short proof of this theorem using<br />
the theory of topological Hochschild homology, which provides a<br />
canonical one-parameter deformation of Hochschild homology in<br />
characteristic p.<br />
<br />
===Andrei Caldararu===<br />
'''Categorical Gromov-Witten invariants beyond genus 1'''<br />
<br />
In a seminal work from 2005 Kevin Costello defined numerical invariants associated to a <br />
Calabi-Yau A-infinity category. These invariants are supposed to generalize the classical<br />
Gromov-Witten invariants (counting curves in a target symplectic manifold) when the category<br />
is taken to be the Fukaya category. In my talk I shall describe some of the ideas involved in Costello's<br />
approach and recent progress (with Junwu Tu) on extending computations of these invariants<br />
past genus 1.<br />
<br />
===Mark Walker===<br />
'''Conjecture D for matrix factorizations'''<br />
<br />
Matrix factorizations form a dg category whose associated homotopy category is equivalent to the stable category of maximum Cohen-Macaulay modules over a hypersurface ring. In the isolated singularity case, the dg category of matrix factorizations is "smooth" and "proper" --- non-commutative analogues of the same-named properties of algebraic varieties. In general, for any smooth and proper dg category, there exist non-commutative analogues of Grothendieck's Standard Conjectures for cycles on smooth and projective varieties. In particular, the non-commutative version of Standard Conjecture D predicts that numerical equivalence and homological equivalence coincide for such a dg category. Recently, Michael Brown and I have proven the non-commutative analogue of Conjecture D for the category of matrix factorizations of an isolated singularity over a field of characteristic 0. In this talk, I will describe our theorem in more detail and give a sense of its proof.<br />
<br />
===Oleksandr Tsymbaliuk===<br />
'''Modified quantum difference Toda systems'''<br />
<br />
The q-version of a Toda system associated with any Lie algebra was introduced independently by Etingof and Sevostyanov in 1999. In this talk, we shall discuss the generalization of this construction which naturally produces a family of 3^{rk(g)-1} similar integrable systems. One of the key ingredients in the proof is played by the fermionic formula for the J-factors (defined as pairing of two Whittaker vectors in Verma modules), due to Feigin-Feigin-Jimbo-Miwa-Mukhin. In types A and C, our construction admits an alternative presentation via local Lax matrices, similar to the classical construction of Faddeev-Takhtajan for the classical type A Toda system. Finally, we shall discuss the geometric interpretation of Whittaker vectors in type A. <br />
<br />
This talk is based on the joint work with M. Finkelberg and R. Gonin.<br />
<br />
===Juliette Bruce===<br />
'''Covering Abelian Varieties and Effective Bertini'''<br />
<br />
I will discuss recent work showing that every abelian variety is covered by a Jacobian whose dimension is bounded. This is joint with Wanlin Li.</div>Adminhttps://www.math.wisc.edu/wiki/index.php?title=Computers&diff=15963Computers2018-09-12T15:22:26Z<p>Admin: </p>
<hr />
<div>== COMPUTING FACILITIES ==<br />
For more detailed information on computing in the Math Department, see [https://sites.google.com/a/wisc.edu/math-intranet/home/computing Math Computing]<br />
<br />
The following facilities are solely for the use of Math Department faculty and graduate students.<br />
<br />
*'''''Computers''''': Graduate students have a Linux machine in each of their offices. Each faculty member has his/her own computer.<br />
<br />
*'''''Public Computers''''': There are two public workstation rooms: 101B and 322. Most of the computers in these rooms use the Linux operating system. In addition, there are Windows machines and scanners in rooms 101 and 322. Most of the computers have combo optical drives. This means that they can read and write to CDs and read from DVDs. Each of the workstation rooms also has a Macintosh running Mac OS X.<br />
<br />
For those instructors wishing to incorporate computers into their lesson plans, the computer classroom, (room B107, featuring 21 Windows machines), is open for reservations. Check with Sharon Paulson in 220 Van Vleck to reserve B107. You can check out the key for B107 from the Math Library.<br />
<br />
*'''''Printers''''': At the end of the halls on floors 3 through 8 and in rooms 101A and B127, there are (double-sided printing) grayscale printers for your use. You can print a total of 250 pages per month on these free of charge. After that, you will be charged 5¢ per page rounded down to the nearest whole dollar amount. Copies from this printer cost 20¢ each with no free copies. <br />
<br />
[[Printing from your laptop]]<br />
<br />
*'''''Other Computer Equipment''''': The Math Department has some laptop computers, several portable computer projectors, and a mobile presentation cart which you can check out from the Math Library with your faculty/staff/student ID card.<br />
<br />
''Ceiling mounted projectors'' are available in rooms 901, B223, B231, B239, B130, B107 and B102. Talk to the computer staff in 515 if you need help using the projectors in 901 and B107. Talk to [mailto:ddombrowski@fpm.wisc.edu Derek Dombrowski ](265-9697) if you need to use the electronic equipment in the other rooms.<br />
<br />
''Wireless'' computing service is available throughout Van Vleck. You will need to open a web browser and type in your NetID and password to use it. Visiting fellows can either use a guest netid (if here for less than 30 days) or use Eduroam instead.<br />
<br />
To find out more about anything listed above, see the website. Send the Computer Staff an email at staff@math.wisc.edu or stop by room 515 between 9:00am and 4:00pm weekdays if you have any questions.</div>Adminhttps://www.math.wisc.edu/wiki/index.php?title=Analysis_Seminar&diff=15256Analysis Seminar2018-03-15T16:08:44Z<p>Admin: /* 2017-2018 Analysis Seminar Schedule */</p>
<hr />
<div>'''Analysis Seminar<br />
'''<br />
<br />
The seminar will meet Tuesdays, 4:00 p.m. in VV B139, unless otherwise indicated.<br />
<br />
If you wish to invite a speaker please contact Betsy at stovall(at)math<br />
<br />
===[[Previous Analysis seminars]]===<br />
<br />
= 2017-2018 Analysis Seminar Schedule =<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
|align="left" | '''institution'''<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 8 in B239 (Colloquium)<br />
| Tess Anderson<br />
| UW Madison<br />
|[[#linktoabstract | A Spherical Maximal Function along the Primes]]<br />
|Tonghai<br />
|-<br />
|September 19<br />
| Brian Street<br />
| UW Madison<br />
|[[#Brian Street | Convenient Coordinates ]]<br />
| Betsy<br />
|-<br />
|September 26<br />
| Hiroyoshi Mitake<br />
| Hiroshima University<br />
|[[#Hiroyoshi Mitake | Derivation of multi-layered interface system and its application ]]<br />
| Hung<br />
|-<br />
|October 3<br />
| Joris Roos<br />
| UW Madison<br />
|[[#Joris Roos | A polynomial Roth theorem on the real line ]]<br />
| Betsy<br />
|-<br />
|October 10<br />
| Michael Greenblatt<br />
| UI Chicago<br />
|[[#Michael Greenblatt | Maximal averages and Radon transforms for two-dimensional hypersurfaces ]]<br />
| Andreas<br />
|-<br />
|October 17<br />
| David Beltran<br />
| Basque Center of Applied Mathematics<br />
|[[#David Beltran | Fefferman-Stein inequalities ]]<br />
| Andreas<br />
|-<br />
|Wednesday, October 18, 4:00 p.m. in B131<br />
|Jonathan Hickman<br />
|University of Chicago<br />
|[[#Jonathan Hickman | Factorising X^n ]]<br />
|Andreas<br />
|-<br />
|October 24<br />
| Xiaochun Li<br />
| UIUC<br />
|[[#Xiaochun Li | Recent progress on the pointwise convergence problems of Schroedinger equations ]]<br />
| Betsy<br />
|-<br />
|Thursday, October 26, 4:30 p.m. in B139<br />
| Fedor Nazarov<br />
| Kent State University<br />
|[[#Fedor Nazarov | The Lerner-Ombrosi-Perez bound in the Muckenhoupt Wheeden conjecture is sharp ]]<br />
| Sergey, Andreas<br />
|-<br />
|Friday, October 27, 4:00 p.m. in B239<br />
| Stefanie Petermichl<br />
| University of Toulouse<br />
|[[#Stefanie Petermichl | Higher order Journé commutators ]]<br />
| Betsy, Andreas<br />
|-<br />
|Wednesday, November 1, 4:00 p.m. in B239 (Colloquium)<br />
| Shaoming Guo<br />
| Indiana University<br />
|[[#Shaoming Guo | Parsell-Vinogradov systems in higher dimensions ]]<br />
| Andreas<br />
|-<br />
|November 14<br />
| Naser Talebizadeh Sardari<br />
| UW Madison<br />
|[[#Naser Talebizadeh Sardari | Quadratic forms and the semiclassical eigenfunction hypothesis ]]<br />
| Betsy<br />
|-<br />
|November 28<br />
| Xianghong Chen<br />
| UW Milwaukee<br />
|[[#Xianghong Chen | Some transfer operators on the circle with trigonometric weights ]]<br />
| Betsy<br />
|-<br />
|Monday, December 4, 4:00, B139<br />
| Bartosz Langowski and Tomasz Szarek<br />
| Institute of Mathematics, Polish Academy of Sciences<br />
|[[#Bartosz Langowski and Tomasz Szarek | Discrete Harmonic Analysis in the Non-Commutative Setting ]]<br />
| Betsy<br />
|-<br />
|Wednesday, December 13, 4:00, B239 (Colloquium)<br />
|Bobby Wilson <br />
|MIT<br />
|[[#Bobby Wilson | Projections in Banach Spaces and Harmonic Analysis ]]<br />
| Andreas<br />
|-<br />
| Monday, February 5, 3:00-3:50, B341 (PDE-GA seminar)<br />
| Andreas Seeger<br />
| UW<br />
|[[#Andreas Seeger | Singular integrals and a problem on mixing flows]] <br />
|<br />
|-<br />
|February 6<br />
| Dong Dong<br />
| UIUC<br />
| [[#Dong Dong | Hibert transforms in a 3 by 3 matrix and applications in number theory]]<br />
|Betsy<br />
|-<br />
|February 13<br />
| Sergey Denisov<br />
| UW Madison<br />
| [[#Sergey Denisov | Spectral Szegő theorem on the real line]]<br />
| <br />
|-<br />
|February 20<br />
| Ruixiang Zhang <br />
| IAS (Princeton)<br />
| [[#Ruixiang Zhang | The (Euclidean) Fractal Uncertainty Principle]]<br />
| Betsy, Jordan, Andreas<br />
|-<br />
|February 27<br />
|Detlef Müller <br />
|University of Kiel<br />
| [[#Detlef Müller | On Fourier restriction for a non-quadratic hyperbolic surface]]<br />
|Betsy, Andreas<br />
|-<br />
|Wednesday, March 7, 4:00 p.m.<br />
| Winfried Sickel <br />
|Friedrich-Schiller-Universität Jena<br />
| [[#Winfried Sickel | On the regularity of compositions of functions]]<br />
|Andreas<br />
|-<br />
|March 13<br />
|<br />
| <br />
| [[#linkofabstract | Title]]<br />
|<br />
|-<br />
|March 20<br />
| Betsy Stovall<br />
| UW<br />
| [[#linkofabstract | Two endpoint bounds via inverse problems]]<br />
|<br />
|-<br />
|April 3<br />
| <br />
| <br />
| [[#linkofabstract | Title]]<br />
|<br />
|-<br />
|April 10<br />
| <br />
| <br />
| [[#linkofabstract | Title]]<br />
|<br />
|-<br />
|Friday, April 13, 4:00 p.m. (Colloquium)<br />
|Jill Pipher<br />
|Brown<br />
| [[#linkofabstract | Title]]<br />
|WIMAW<br />
|-<br />
|April 17<br />
| <br />
| <br />
| [[#linkofabstract | Title]]<br />
|<br />
|-<br />
|April 24<br />
| Lenka Slavíková<br />
| University of Missouri<br />
| [[#linkofabstract | TBA]]<br />
|Betsy, Andreas<br />
|-<br />
|May 1<br />
| Xianghong Gong<br />
| UW<br />
| [[#linkofabstract | Title]]<br />
|<br />
|-<br />
|May 15<br />
|Gennady Uraltsev<br />
|Cornell University<br />
| [[#linkofabstract | TBA]]<br />
|Betsy, Andreas<br />
|-<br />
| May 16-18, [http://www.math.wisc.edu/~stovall/FA2018/ Workshop in Fourier Analysis]<br />
|<br />
|<br />
|<br />
|Betsy, Andreas<br />
|-<br />
|}<br />
<br />
=Abstracts=<br />
===Brian Street===<br />
<br />
Title: Convenient Coordinates<br />
<br />
Abstract: We discuss the method of picking a convenient coordinate system adapted to vector fields. Let X_1,...,X_q be either real or complex C^1 vector fields. We discuss the question of when there is a coordinate system in which the vector fields are smoother (e.g., C^m, or C^\infty, or real analytic). By answering this in a quantitative way, we obtain coordinate charts which can be used as generalized scaling maps. When the vector fields are real this is joint work with Stovall, and continues in the line of quantitative sub-Riemannian geometry initiated by Nagel, Stein, and Wainger. When the vector fields are complex one obtains a geometry with more structure which can be thought of as "sub-Hermitian".<br />
<br />
===Hiroyoshi Mitake===<br />
<br />
Title: Derivation of multi-layered interface system and its application<br />
<br />
Abstract: In this talk, I will propose a multi-layered interface system which can <br />
be formally derived by the singular limit of the weakly coupled system of <br />
the Allen-Cahn equation. By using the level set approach, this system can be <br />
written as a quasi-monotone degenerate parabolic system. <br />
We give results of the well-posedness of viscosity solutions, and study the <br />
singularity of each layers. This is a joint work with H. Ninomiya, K. Todoroki.<br />
<br />
===Joris Roos===<br />
<br />
Title: A polynomial Roth theorem on the real line<br />
<br />
Abstract: For a polynomial P of degree greater than one, we show the existence of patterns of the form (x,x+t,x+P(t)) with a gap estimate on t in positive density subsets of the reals. This is an extension of an earlier result of Bourgain. Our proof is a combination of Bourgain’s approach and more recent methods that were originally developed for the study of the bilinear Hilbert transform along curves. This talk is based on a joint work with Polona Durcik and Shaoming Guo.<br />
<br />
===Michael Greenblatt===<br />
<br />
Title: Maximal averages and Radon transforms for two-dimensional hypersurfaces<br />
<br />
Abstract: A general local result concerning L^p boundedness of maximal averages over 2D hypersurfaces is described, where p > 2. The surfaces are allowed to have either the traditional smooth density function or a singularity growing as |(x,y)|^{-t} for some 0 < t < 2. This result is a generalization of a theorem of Ikromov, Kempe, and Mueller. Similar methods can be used to show sharp L^p to L^p_a Sobolev estimates for associated Radon transform operators when p is in a certain interval containing 2.<br />
<br />
===David Beltran===<br />
<br />
Title: Fefferman Stein Inequalities<br />
<br />
Abstract: Given an operator T, we focus on obtaining two-weighted inequalities in which the weights are related via certain maximal function. These inequalites, which originated in work of Fefferman and Stein, have been established in an optimal way for different classical operators in Harmonic Analysis. In this talk, we survey some classical results and we present some recent Fefferman-Stein inequalities for pseudodifferential operators and for the solution operators to dispersive equations.<br />
<br />
===Jonathan Hickman===<br />
<br />
Title: Factorising X^n.<br />
<br />
Question: how many ways can the polynomial $X^n$ be factorised as a product of linear factors? Answer: it depends on the ring... In this talk I will describe joint work with Jim Wright investigating certain exponential sum estimates over rings of integers modulo N. This theory serves as a discrete analogue of the (euclidean) Fourier restriction problem, a central question in contemporary harmonic analysis. In particular, as part of this study, the question of counting the number of factorisations of polynomials over such rings naturally arises. I will describe how these number-theoretic considerations can themselves be approached via methods from harmonic analysis.<br />
<br />
===Xiaochun Li ===<br />
<br />
Title: Recent progress on the pointwise convergence problems of Schrodinger equations<br />
<br />
Abstract: Recently, Guth, Du and I solved the pointwise convergence problem of Schrodinger equations in two-dimensional case. We proved that the solution to free Schrodinger equation in R^2 converges to its initial data, provided the initial data belongs to H^s for s larger than 1/3. This result is sharp, up to the end point, due to Bourgain's example. The proof relies on the polynomial partitioning method and the decoupling method. In addition, the pointwise convergence problem is closely related to Fourier restriction conjecture.<br />
<br />
===Fedor Nazarov=== <br />
<br />
Title: The Lerner-Ombrosi-Perez bound in the Muckenhoupt-Wheeden<br />
conjecture is sharp.<br />
<br />
Abstract: We show that the upper bound $[w]_{A_1}\log (e+[w]_{A_1})$ for<br />
the norm of the Hilbert transform on the line as an operator from $L^1(w)$<br />
to $L^{1,\infty}(w)$ cannot be improved in general. This is a joint work<br />
with Andrei Lerner and Sheldy Ombrosi.<br />
<br />
===Stefanie Petermichl===<br />
Title: Higher order Journé commutators<br />
<br />
Abstract: We consider questions that stem from operator theory via Hankel and<br />
Toeplitz forms and target (weak) factorisation of Hardy spaces. In<br />
more basic terms, let us consider a function on the unit circle in its<br />
Fourier representation. Let P_+ denote the projection onto<br />
non-negative and P_- onto negative frequencies. Let b denote<br />
multiplication by the symbol function b. It is a classical theorem by<br />
Nehari that the composed operator P_+ b P_- is bounded on L^2 if and<br />
only if b is in an appropriate space of functions of bounded mean<br />
oscillation. The necessity makes use of a classical factorisation<br />
theorem of complex function theory on the disk. This type of question<br />
can be reformulated in terms of commutators [b,H]=bH-Hb with the<br />
Hilbert transform H=P_+ - P_- . Whenever factorisation is absent, such<br />
as in the real variable setting, in the multi-parameter setting or<br />
other, these classifications can be very difficult.<br />
<br />
Such lines were begun by Coifman, Rochberg, Weiss (real variables) and<br />
by Cotlar, Ferguson, Sadosky (multi-parameter) of characterisation of<br />
spaces of bounded mean oscillation via L^p boundedness of commutators.<br />
We present here an endpoint to this theory, bringing all such<br />
characterisation results under one roof.<br />
<br />
The tools used go deep into modern advances in dyadic harmonic<br />
analysis, while preserving the Ansatz from classical operator theory.<br />
<br />
===Shaoming Guo ===<br />
Title: Parsell-Vinogradov systems in higher dimensions<br />
<br />
Abstract: <br />
I will present a few results on counting the numbers of integer solutions of Parsell-Vinogradov systems in higher dimensions.<br />
Applications to Waring’s problem and to the problem of counting rational linear subspaces lying on certain hyper-surface will be discussed.<br />
Joint works with Jean Bourgain, Ciprian Demeter and Ruixiang Zhang.<br />
<br />
===Naser Talebizadeh Sardari===<br />
<br />
Title: Quadratic forms and the semiclassical eigenfunction hypothesis<br />
<br />
Abstract: Let <math>Q(X)</math> be any integral primitive positive definite quadratic form in <math>k</math> variables, where <math>k\geq4</math>, and discriminant <math>D</math>. For any integer <math>n</math>, we give an upper bound on the number of integral solutions of <math>Q(X)=n</math> in terms of <math>n</math>, <math>k</math>, and <math>D</math>. As a corollary, we prove a conjecture of Lester and Rudnick on the small scale equidistribution of almost all functions belonging to any orthonormal basis of a given eigenspace of the Laplacian on the flat torus <math>\mathbb{T}^d</math> for <math>d\geq 5</math>. This conjecture is motivated by the work of Berry\cite{Berry, Michael} on semiclassical eigenfunction hypothesis.<br />
<br />
===Xianghong Chen===<br />
<br />
Title: Some transfer operators on the circle with trigonometric weights<br />
<br />
Abstract: A transfer operator is an averaging operator over the preimages of a given map. Certain dynamical properties of the map can be studied through its associated transfer operator. In this talk we will introduce a class of weighted transfer operators associated to the Bernoulli maps on the circle (i.e. multiplication by a given integer, mod 1). We will illustrate how the spectral properties of these operators may depend on the specific weight chosen and demonstrate multiple phase transitions. We also present some results on evaluating the spectral radii and corresponding eigenfunctions of these operators, as well as their connections to Fourier analysis. This is joint work with Hans Volkmer. <br />
<br />
===Bobby Wilson===<br />
<br />
Title: Projections in Banach Spaces and Harmonic Analysis<br />
<br />
Abstract: In this talk, we will discuss the measure theoretic principles of orthogonal projections that follow from the classical Besicovitch-Federer projection theorem. The Besicovitch-Federer projection theorem offers a characterization of rectifiability of one-dimensional sets in R^d by the size of their projections to lines. We will focus on the validity of analogues to the Besicovitch-Federer projection theorem with respect to such sets in general Banach spaces. In particular, we will show that the projection theorem is false when the Banach space is infinite-dimensional and discuss related applications to questions in Harmonic Analysis. This is joint work with Marianna Csornyei and David Bate.<br />
<br />
===Andreas Seeger===<br />
<br />
Title: Singular integrals and a problem on mixing flows<br />
<br />
Abstract: The talk will be about results related to Bressan's mixing problem. We present an inequality for the change of a Bianchini semi-norm of characteristic functions under the flow generated by a divergence free time dependent vector field. The approach leads to a bilinear singular integral operator for which one proves bounds on Hardy spaces. This is joint work with Mahir Hadžić, Charles Smart and Brian Street.<br />
<br />
===Dong Dong===<br />
<br />
Title: Hibert transforms in a 3 by 3 matrix and applications in number theory<br />
<br />
Abstract: This talk could interest both analysts and number theorists. I will first present 35 variants of Hilbert transforms, with a focus on their connections with ergodic theory, number theory, and combinatorics. Then I will show how to use Fourier analysis tools to reduce a number theory problem (Roth theorem) to an algebraic geometry problem: this joint work Li and Sawin fully answers a question of Bourgain and Chang about three-term polynomial progressions in subsets of finite fields. I guarantee that a second-year graduate student can understand at least 50% of the talk.<br />
<br />
===Sergey Denisov===<br />
<br />
Title: Spectral Szegő theorem on the real line<br />
<br />
Abstract: For even measures on the real line, we give the criterion for the logarithmic integral to converge in terms of the corresponding De-Branges system (or Krein's string). The applications to probability (linear prediction for stationary Gaussian processes) will be explained. This is the joint result with R. Bessonov.<br />
<br />
===Ruixiang Zhang===<br />
<br />
Title: The (Euclidean) Fractal Uncertainty Principle<br />
<br />
Abstract: On the real line, a version of the uncertainty principle says: If a nonzero function f has its Fourier support lying in B and |A||B| is much smaller than 1, then the L^2 norm of f on A cannot be close to the whole L^2 norm of f. Recently, Bourgain and Dyatlov proved a Fractal Uncertainty Principle (FUP) which has a similar statement. The difference is that in FUP the product of |A| and |B| can be much bigger, but A and B both have to be porous at many scales. We will introduce the theorem and then discuss some unusual features of its proof, most notably the application of the Beurling-Malliavin Theorem. In the original work the dependence on the dimensions of both fractals was ineffective. We will also discuss why we can overcome this ineffectivity (joint work with Long Jin).<br />
<br />
===Detlef Müller===<br />
<br />
Title: On Fourier restriction for a non-quadratic hyperbolic surface<br />
<br />
Abstract: In contrast to what is known about Fourier restriction for elliptic surfaces, rather little is known about hyperbolic surfaces. Hitherto, basically only the quadric $z=xy$ had been studied successfully. In my talk, after giving some background on Fourier restriction, I shall report on recent joint work with S. Buschenhenke and A. Vargas on a cubic perturbation of this quadric. Our analysis reveals that the geometry of the problem changes drastically in the presence of a perturbation term, and that new techniques, compared to the elliptic case, are required to handle more general hyperbolic surfaces.<br />
<br />
===Winfried Sickel===<br />
<br />
Title: On the regularity of compositions of functions<br />
<br />
Abstract: Let <math>E</math> denote a Banach space of locally integrable functions on <math>\mathbb{R}</math>. To each continuous function <math>f:\mathbb{R} \to \mathbb{R}</math><br />
we associate the composition operator<br />
<math>T_f(g):= f\circ g</math>, <math>g\in E</math>. <br />
The properties of <math>T_f</math> strongly depend on the chosen function space <math>E</math>.<br />
In my talk I will concentrate on Sobolev spaces <math>W^m_p</math> and Slobodeckij spaces <math>W^s_p</math>.<br />
The main aim will consist in giving a survey on necessary and sufficient conditions on <math>f</math><br />
such that the composition operator maps such a space <math>E</math> into itself.<br />
<br />
=Extras=<br />
[[Blank Analysis Seminar Template]]</div>Adminhttps://www.math.wisc.edu/wiki/index.php?title=Analysis_Seminar&diff=15255Analysis Seminar2018-03-15T16:08:18Z<p>Admin: </p>
<hr />
<div>'''Analysis Seminar<br />
'''<br />
<br />
The seminar will meet Tuesdays, 4:00 p.m. in VV B139, unless otherwise indicated.<br />
<br />
If you wish to invite a speaker please contact Betsy at stovall(at)math<br />
<br />
===[[Previous Analysis seminars]]===<br />
<br />
= 2017-2018 Analysis Seminar Schedule =<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
|align="left" | '''institution'''<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 8 in B239 (Colloquium)<br />
| Tess Anderson<br />
| UW Madison<br />
|[[#linktoabstract | A Spherical Maximal Function along the Primes]]<br />
|Tonghai<br />
|-<br />
|September 19<br />
| Brian Street<br />
| UW Madison<br />
|[[#Brian Street | Convenient Coordinates ]]<br />
| Betsy<br />
|-<br />
|September 26<br />
| Hiroyoshi Mitake<br />
| Hiroshima University<br />
|[[#Hiroyoshi Mitake | Derivation of multi-layered interface system and its application ]]<br />
| Hung<br />
|-<br />
|October 3<br />
| Joris Roos<br />
| UW Madison<br />
|[[#Joris Roos | A polynomial Roth theorem on the real line ]]<br />
| Betsy<br />
|-<br />
|October 10<br />
| Michael Greenblatt<br />
| UI Chicago<br />
|[[#Michael Greenblatt | Maximal averages and Radon transforms for two-dimensional hypersurfaces ]]<br />
| Andreas<br />
|-<br />
|October 17<br />
| David Beltran<br />
| Basque Center of Applied Mathematics<br />
|[[#David Beltran | Fefferman-Stein inequalities ]]<br />
| Andreas<br />
|-<br />
|Wednesday, October 18, 4:00 p.m. in B131<br />
|Jonathan Hickman<br />
|University of Chicago<br />
|[[#Jonathan Hickman | Factorising X^n ]]<br />
|Andreas<br />
|-<br />
|October 24<br />
| Xiaochun Li<br />
| UIUC<br />
|[[#Xiaochun Li | Recent progress on the pointwise convergence problems of Schroedinger equations ]]<br />
| Betsy<br />
|-<br />
|Thursday, October 26, 4:30 p.m. in B139<br />
| Fedor Nazarov<br />
| Kent State University<br />
|[[#Fedor Nazarov | The Lerner-Ombrosi-Perez bound in the Muckenhoupt Wheeden conjecture is sharp ]]<br />
| Sergey, Andreas<br />
|-<br />
|Friday, October 27, 4:00 p.m. in B239<br />
| Stefanie Petermichl<br />
| University of Toulouse<br />
|[[#Stefanie Petermichl | Higher order Journé commutators ]]<br />
| Betsy, Andreas<br />
|-<br />
|Wednesday, November 1, 4:00 p.m. in B239 (Colloquium)<br />
| Shaoming Guo<br />
| Indiana University<br />
|[[#Shaoming Guo | Parsell-Vinogradov systems in higher dimensions ]]<br />
| Andreas<br />
|-<br />
|November 14<br />
| Naser Talebizadeh Sardari<br />
| UW Madison<br />
|[[#Naser Talebizadeh Sardari | Quadratic forms and the semiclassical eigenfunction hypothesis ]]<br />
| Betsy<br />
|-<br />
|November 28<br />
| Xianghong Chen<br />
| UW Milwaukee<br />
|[[#Xianghong Chen | Some transfer operators on the circle with trigonometric weights ]]<br />
| Betsy<br />
|-<br />
|Monday, December 4, 4:00, B139<br />
| Bartosz Langowski and Tomasz Szarek<br />
| Institute of Mathematics, Polish Academy of Sciences<br />
|[[#Bartosz Langowski and Tomasz Szarek | Discrete Harmonic Analysis in the Non-Commutative Setting ]]<br />
| Betsy<br />
|-<br />
|Wednesday, December 13, 4:00, B239 (Colloquium)<br />
|Bobby Wilson <br />
|MIT<br />
|[[#Bobby Wilson | Projections in Banach Spaces and Harmonic Analysis ]]<br />
| Andreas<br />
|-<br />
| Monday, February 5, 3:00-3:50, B341 (PDE-GA seminar)<br />
| Andreas Seeger<br />
| UW<br />
|[[#Andreas Seeger | Singular integrals and a problem on mixing flows]] <br />
|<br />
|-<br />
|February 6<br />
| Dong Dong<br />
| UIUC<br />
| [[#Dong Dong | Hibert transforms in a 3 by 3 matrix and applications in number theory]]<br />
|Betsy<br />
|-<br />
|February 13<br />
| Sergey Denisov<br />
| UW Madison<br />
| [[#Sergey Denisov | Spectral Szegő theorem on the real line]]<br />
| <br />
|-<br />
|February 20<br />
| Ruixiang Zhang <br />
| IAS (Princeton)<br />
| [[#Ruixiang Zhang | The (Euclidean) Fractal Uncertainty Principle]]<br />
| Betsy, Jordan, Andreas<br />
|-<br />
|February 27<br />
|Detlef Müller <br />
|University of Kiel<br />
| [[#Detlef Müller | On Fourier restriction for a non-quadratic hyperbolic surface]]<br />
|Betsy, Andreas<br />
|-<br />
|Wednesday, March 7, 4:00 p.m.<br />
| Winfried Sickel <br />
|Friedrich-Schiller-Universität Jena<br />
| [[#Winfried Sickel | On the regularity of compositions of functions]]<br />
|Andreas<br />
|-<br />
|March 13<br />
|<br />
| <br />
| [[#linkofabstract | Title]]<br />
|<br />
|-<br />
|March 20<br />
| Betsy Stovall<br />
| Two endpoint bounds via inverse problems<br />
| [[#linkofabstract | Title]]<br />
|<br />
|-<br />
|April 3<br />
| <br />
| <br />
| [[#linkofabstract | Title]]<br />
|<br />
|-<br />
|April 10<br />
| <br />
| <br />
| [[#linkofabstract | Title]]<br />
|<br />
|-<br />
|Friday, April 13, 4:00 p.m. (Colloquium)<br />
|Jill Pipher<br />
|Brown<br />
| [[#linkofabstract | Title]]<br />
|WIMAW<br />
|-<br />
|April 17<br />
| <br />
| <br />
| [[#linkofabstract | Title]]<br />
|<br />
|-<br />
|April 24<br />
| Lenka Slavíková<br />
| University of Missouri<br />
| [[#linkofabstract | TBA]]<br />
|Betsy, Andreas<br />
|-<br />
|May 1<br />
| Xianghong Gong<br />
| UW<br />
| [[#linkofabstract | Title]]<br />
|<br />
|-<br />
|May 15<br />
|Gennady Uraltsev<br />
|Cornell University<br />
| [[#linkofabstract | TBA]]<br />
|Betsy, Andreas<br />
|-<br />
| May 16-18, [http://www.math.wisc.edu/~stovall/FA2018/ Workshop in Fourier Analysis]<br />
|<br />
|<br />
|<br />
|Betsy, Andreas<br />
|-<br />
|}<br />
<br />
=Abstracts=<br />
===Brian Street===<br />
<br />
Title: Convenient Coordinates<br />
<br />
Abstract: We discuss the method of picking a convenient coordinate system adapted to vector fields. Let X_1,...,X_q be either real or complex C^1 vector fields. We discuss the question of when there is a coordinate system in which the vector fields are smoother (e.g., C^m, or C^\infty, or real analytic). By answering this in a quantitative way, we obtain coordinate charts which can be used as generalized scaling maps. When the vector fields are real this is joint work with Stovall, and continues in the line of quantitative sub-Riemannian geometry initiated by Nagel, Stein, and Wainger. When the vector fields are complex one obtains a geometry with more structure which can be thought of as "sub-Hermitian".<br />
<br />
===Hiroyoshi Mitake===<br />
<br />
Title: Derivation of multi-layered interface system and its application<br />
<br />
Abstract: In this talk, I will propose a multi-layered interface system which can <br />
be formally derived by the singular limit of the weakly coupled system of <br />
the Allen-Cahn equation. By using the level set approach, this system can be <br />
written as a quasi-monotone degenerate parabolic system. <br />
We give results of the well-posedness of viscosity solutions, and study the <br />
singularity of each layers. This is a joint work with H. Ninomiya, K. Todoroki.<br />
<br />
===Joris Roos===<br />
<br />
Title: A polynomial Roth theorem on the real line<br />
<br />
Abstract: For a polynomial P of degree greater than one, we show the existence of patterns of the form (x,x+t,x+P(t)) with a gap estimate on t in positive density subsets of the reals. This is an extension of an earlier result of Bourgain. Our proof is a combination of Bourgain’s approach and more recent methods that were originally developed for the study of the bilinear Hilbert transform along curves. This talk is based on a joint work with Polona Durcik and Shaoming Guo.<br />
<br />
===Michael Greenblatt===<br />
<br />
Title: Maximal averages and Radon transforms for two-dimensional hypersurfaces<br />
<br />
Abstract: A general local result concerning L^p boundedness of maximal averages over 2D hypersurfaces is described, where p > 2. The surfaces are allowed to have either the traditional smooth density function or a singularity growing as |(x,y)|^{-t} for some 0 < t < 2. This result is a generalization of a theorem of Ikromov, Kempe, and Mueller. Similar methods can be used to show sharp L^p to L^p_a Sobolev estimates for associated Radon transform operators when p is in a certain interval containing 2.<br />
<br />
===David Beltran===<br />
<br />
Title: Fefferman Stein Inequalities<br />
<br />
Abstract: Given an operator T, we focus on obtaining two-weighted inequalities in which the weights are related via certain maximal function. These inequalites, which originated in work of Fefferman and Stein, have been established in an optimal way for different classical operators in Harmonic Analysis. In this talk, we survey some classical results and we present some recent Fefferman-Stein inequalities for pseudodifferential operators and for the solution operators to dispersive equations.<br />
<br />
===Jonathan Hickman===<br />
<br />
Title: Factorising X^n.<br />
<br />
Question: how many ways can the polynomial $X^n$ be factorised as a product of linear factors? Answer: it depends on the ring... In this talk I will describe joint work with Jim Wright investigating certain exponential sum estimates over rings of integers modulo N. This theory serves as a discrete analogue of the (euclidean) Fourier restriction problem, a central question in contemporary harmonic analysis. In particular, as part of this study, the question of counting the number of factorisations of polynomials over such rings naturally arises. I will describe how these number-theoretic considerations can themselves be approached via methods from harmonic analysis.<br />
<br />
===Xiaochun Li ===<br />
<br />
Title: Recent progress on the pointwise convergence problems of Schrodinger equations<br />
<br />
Abstract: Recently, Guth, Du and I solved the pointwise convergence problem of Schrodinger equations in two-dimensional case. We proved that the solution to free Schrodinger equation in R^2 converges to its initial data, provided the initial data belongs to H^s for s larger than 1/3. This result is sharp, up to the end point, due to Bourgain's example. The proof relies on the polynomial partitioning method and the decoupling method. In addition, the pointwise convergence problem is closely related to Fourier restriction conjecture.<br />
<br />
===Fedor Nazarov=== <br />
<br />
Title: The Lerner-Ombrosi-Perez bound in the Muckenhoupt-Wheeden<br />
conjecture is sharp.<br />
<br />
Abstract: We show that the upper bound $[w]_{A_1}\log (e+[w]_{A_1})$ for<br />
the norm of the Hilbert transform on the line as an operator from $L^1(w)$<br />
to $L^{1,\infty}(w)$ cannot be improved in general. This is a joint work<br />
with Andrei Lerner and Sheldy Ombrosi.<br />
<br />
===Stefanie Petermichl===<br />
Title: Higher order Journé commutators<br />
<br />
Abstract: We consider questions that stem from operator theory via Hankel and<br />
Toeplitz forms and target (weak) factorisation of Hardy spaces. In<br />
more basic terms, let us consider a function on the unit circle in its<br />
Fourier representation. Let P_+ denote the projection onto<br />
non-negative and P_- onto negative frequencies. Let b denote<br />
multiplication by the symbol function b. It is a classical theorem by<br />
Nehari that the composed operator P_+ b P_- is bounded on L^2 if and<br />
only if b is in an appropriate space of functions of bounded mean<br />
oscillation. The necessity makes use of a classical factorisation<br />
theorem of complex function theory on the disk. This type of question<br />
can be reformulated in terms of commutators [b,H]=bH-Hb with the<br />
Hilbert transform H=P_+ - P_- . Whenever factorisation is absent, such<br />
as in the real variable setting, in the multi-parameter setting or<br />
other, these classifications can be very difficult.<br />
<br />
Such lines were begun by Coifman, Rochberg, Weiss (real variables) and<br />
by Cotlar, Ferguson, Sadosky (multi-parameter) of characterisation of<br />
spaces of bounded mean oscillation via L^p boundedness of commutators.<br />
We present here an endpoint to this theory, bringing all such<br />
characterisation results under one roof.<br />
<br />
The tools used go deep into modern advances in dyadic harmonic<br />
analysis, while preserving the Ansatz from classical operator theory.<br />
<br />
===Shaoming Guo ===<br />
Title: Parsell-Vinogradov systems in higher dimensions<br />
<br />
Abstract: <br />
I will present a few results on counting the numbers of integer solutions of Parsell-Vinogradov systems in higher dimensions.<br />
Applications to Waring’s problem and to the problem of counting rational linear subspaces lying on certain hyper-surface will be discussed.<br />
Joint works with Jean Bourgain, Ciprian Demeter and Ruixiang Zhang.<br />
<br />
===Naser Talebizadeh Sardari===<br />
<br />
Title: Quadratic forms and the semiclassical eigenfunction hypothesis<br />
<br />
Abstract: Let <math>Q(X)</math> be any integral primitive positive definite quadratic form in <math>k</math> variables, where <math>k\geq4</math>, and discriminant <math>D</math>. For any integer <math>n</math>, we give an upper bound on the number of integral solutions of <math>Q(X)=n</math> in terms of <math>n</math>, <math>k</math>, and <math>D</math>. As a corollary, we prove a conjecture of Lester and Rudnick on the small scale equidistribution of almost all functions belonging to any orthonormal basis of a given eigenspace of the Laplacian on the flat torus <math>\mathbb{T}^d</math> for <math>d\geq 5</math>. This conjecture is motivated by the work of Berry\cite{Berry, Michael} on semiclassical eigenfunction hypothesis.<br />
<br />
===Xianghong Chen===<br />
<br />
Title: Some transfer operators on the circle with trigonometric weights<br />
<br />
Abstract: A transfer operator is an averaging operator over the preimages of a given map. Certain dynamical properties of the map can be studied through its associated transfer operator. In this talk we will introduce a class of weighted transfer operators associated to the Bernoulli maps on the circle (i.e. multiplication by a given integer, mod 1). We will illustrate how the spectral properties of these operators may depend on the specific weight chosen and demonstrate multiple phase transitions. We also present some results on evaluating the spectral radii and corresponding eigenfunctions of these operators, as well as their connections to Fourier analysis. This is joint work with Hans Volkmer. <br />
<br />
===Bobby Wilson===<br />
<br />
Title: Projections in Banach Spaces and Harmonic Analysis<br />
<br />
Abstract: In this talk, we will discuss the measure theoretic principles of orthogonal projections that follow from the classical Besicovitch-Federer projection theorem. The Besicovitch-Federer projection theorem offers a characterization of rectifiability of one-dimensional sets in R^d by the size of their projections to lines. We will focus on the validity of analogues to the Besicovitch-Federer projection theorem with respect to such sets in general Banach spaces. In particular, we will show that the projection theorem is false when the Banach space is infinite-dimensional and discuss related applications to questions in Harmonic Analysis. This is joint work with Marianna Csornyei and David Bate.<br />
<br />
===Andreas Seeger===<br />
<br />
Title: Singular integrals and a problem on mixing flows<br />
<br />
Abstract: The talk will be about results related to Bressan's mixing problem. We present an inequality for the change of a Bianchini semi-norm of characteristic functions under the flow generated by a divergence free time dependent vector field. The approach leads to a bilinear singular integral operator for which one proves bounds on Hardy spaces. This is joint work with Mahir Hadžić, Charles Smart and Brian Street.<br />
<br />
===Dong Dong===<br />
<br />
Title: Hibert transforms in a 3 by 3 matrix and applications in number theory<br />
<br />
Abstract: This talk could interest both analysts and number theorists. I will first present 35 variants of Hilbert transforms, with a focus on their connections with ergodic theory, number theory, and combinatorics. Then I will show how to use Fourier analysis tools to reduce a number theory problem (Roth theorem) to an algebraic geometry problem: this joint work Li and Sawin fully answers a question of Bourgain and Chang about three-term polynomial progressions in subsets of finite fields. I guarantee that a second-year graduate student can understand at least 50% of the talk.<br />
<br />
===Sergey Denisov===<br />
<br />
Title: Spectral Szegő theorem on the real line<br />
<br />
Abstract: For even measures on the real line, we give the criterion for the logarithmic integral to converge in terms of the corresponding De-Branges system (or Krein's string). The applications to probability (linear prediction for stationary Gaussian processes) will be explained. This is the joint result with R. Bessonov.<br />
<br />
===Ruixiang Zhang===<br />
<br />
Title: The (Euclidean) Fractal Uncertainty Principle<br />
<br />
Abstract: On the real line, a version of the uncertainty principle says: If a nonzero function f has its Fourier support lying in B and |A||B| is much smaller than 1, then the L^2 norm of f on A cannot be close to the whole L^2 norm of f. Recently, Bourgain and Dyatlov proved a Fractal Uncertainty Principle (FUP) which has a similar statement. The difference is that in FUP the product of |A| and |B| can be much bigger, but A and B both have to be porous at many scales. We will introduce the theorem and then discuss some unusual features of its proof, most notably the application of the Beurling-Malliavin Theorem. In the original work the dependence on the dimensions of both fractals was ineffective. We will also discuss why we can overcome this ineffectivity (joint work with Long Jin).<br />
<br />
===Detlef Müller===<br />
<br />
Title: On Fourier restriction for a non-quadratic hyperbolic surface<br />
<br />
Abstract: In contrast to what is known about Fourier restriction for elliptic surfaces, rather little is known about hyperbolic surfaces. Hitherto, basically only the quadric $z=xy$ had been studied successfully. In my talk, after giving some background on Fourier restriction, I shall report on recent joint work with S. Buschenhenke and A. Vargas on a cubic perturbation of this quadric. Our analysis reveals that the geometry of the problem changes drastically in the presence of a perturbation term, and that new techniques, compared to the elliptic case, are required to handle more general hyperbolic surfaces.<br />
<br />
===Winfried Sickel===<br />
<br />
Title: On the regularity of compositions of functions<br />
<br />
Abstract: Let <math>E</math> denote a Banach space of locally integrable functions on <math>\mathbb{R}</math>. To each continuous function <math>f:\mathbb{R} \to \mathbb{R}</math><br />
we associate the composition operator<br />
<math>T_f(g):= f\circ g</math>, <math>g\in E</math>. <br />
The properties of <math>T_f</math> strongly depend on the chosen function space <math>E</math>.<br />
In my talk I will concentrate on Sobolev spaces <math>W^m_p</math> and Slobodeckij spaces <math>W^s_p</math>.<br />
The main aim will consist in giving a survey on necessary and sufficient conditions on <math>f</math><br />
such that the composition operator maps such a space <math>E</math> into itself.<br />
<br />
=Extras=<br />
[[Blank Analysis Seminar Template]]</div>Adminhttps://www.math.wisc.edu/wiki/index.php?title=Cookie_seminar&diff=8460Cookie seminar2014-09-26T18:24:37Z<p>Admin: /* Monday, January 28, Will Mitchell */</p>
<hr />
<div>'''General Information''': Cookie seminar will take place on Mondays at 3:30 in the 9th floor lounge area. Talks should be of interest to the general math community, and generally will not run longer then 20 minutes. Everyone is welcome to talk, please just sign up on this page. Alternatively I will also sign interested people up at the seminar itself. As one would expect from the title there will generally be cookies provided, although the snack may vary from week to week. <br />
<br />
To sign up please provide your name and a title. Abstracts are welcome but optional.<br />
<br />
<br />
==Spring 2013==<br />
<br />
==Monday, January 28, Will Mitchell==<br />
<br />
<br />
Title: an unsolved graph isomorphism problem from plane geometry<br />
<br />
Abstract: A geometric 4-configuration is a collection of <math>$n$</math> lines and $n$ points in<br />
the Euclidean plane with the property that each of the lines passes through exactly four<br />
of the points, and each of the points lies on exactly four of the lines. No<br />
illustration of a 4-configuration appeared in print until 1980. The so-called<br />
"celestial configurations" are a well-behaved family of these objects. After discussing<br />
the construction and nomenclature of the celestial configurations, I'll describe an open<br />
problem regarding their graph-theoretical properties.<br />
<br />
==Monday, February 4, Paul Tveite==<br />
<br />
<br />
Math and redistricting: Redrawing of congressional districts in the US is a<br />
political process with interesting results. It's also an interesting<br />
mathematical problem. I'll introduce a couple measures of irregularity of<br />
districts and a couple algorithms for objectively drawing district lines.<br />
<br />
<br />
<br />
==Monday, February 18, Diane Holcomb==<br />
<br />
Title: The mathematics of apportionment<br />
<br />
Abstract: Every year the United States conducts a census and then gives out or apportions seats in the House of Representatives to each of the states according to its population, unfortunately the constitution doesn't provide much guidance on how exactly to do this. I'll go over a bit of the history of how the US has apportioned the seats in the House and some of the math behind the different methods. <br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
==Monday, March 11, David Diamondstone==<br />
<br />
Title: "pi" in different metrics<br />
<br />
Abstract: In honor of pi day, we will explore the other values pi might have had, if we lived with a non-Euclidean metric. Examples include the universe of Carl Sagan's ''Contact'', surfaces of constant curvature, and metrics which arise from norms on '''R'''<sup>2</sup>.</div>Adminhttps://www.math.wisc.edu/wiki/index.php?title=Probability_Seminar&diff=8459Probability Seminar2014-09-26T18:07:20Z<p>Admin: </p>
<hr />
<div>__NOTOC__<br />
<br />
= Fall 2014 =<br />
<br />
<br />
<br />
<b>Thursdays in 901 Van Vleck Hall at 2:25 PM</b>, unless otherwise noted. <br />
<br />
<b><br />
If you would like to sign up for the email list to receive seminar announcements then please send an email to join-probsem@lists.wisc.edu.<br />
<br />
<!-- [[File:probsem.jpg]] --><br />
</b><br />
<br />
= =<br />
<br />
== Thursday, September 11, <span style="color:red">Van Vleck B105,</span> [http://www.math.wisc.edu/~mmwood/ Melanie Matchett Wood], UW-Madison ==<br />
<br />
Please note the non-standard room.<br />
<br />
Title: '''The distribution of sandpile groups of random graphs'''<br />
<br />
Abstract:<br><br />
The sandpile group is an abelian group associated to a graph, given as<br />
the cokernel of the graph Laplacian. An Erdős–Rényi random graph<br />
then gives some distribution of random abelian groups. We will give<br />
an introduction to various models of random finite abelian groups<br />
arising in number theory and the connections to the distribution<br />
conjectured by Payne et. al. for sandpile groups. We will talk about<br />
the moments of random finite abelian groups, and how in practice these<br />
are often more accessible than the distributions themselves, but<br />
frustratingly are not a priori guaranteed to determine the<br />
distribution. In this case however, we have found the moments of the<br />
sandpile groups of random graphs, and proved they determine the<br />
measure, and have proven Payne's conjecture.<br />
<br />
== Thursday, September 18, [http://www.math.purdue.edu/~peterson/ Jonathon Peterson], [http://www.math.purdue.edu/ Purdue University] ==<br />
<br />
Title: '''Hydrodynamic limits for directed traps and systems of independent RWRE'''<br />
<br />
Abstract:<br />
<br />
We study the evolution of a system of independent random walks in a common random environment (RWRE). Previously a hydrodynamic limit was proved in the case where the environment is such that the random walks are ballistic (i.e., transient with non-zero speed <math>$v_0 \neq 0$)</math>. In this case it was shown that the asymptotic particle density is simply translated deterministically by the speed $v_0$. In this talk we will consider the more difficult case of RWRE that are transient but with $v_0=0$. Under the appropriate space-time scaling, we prove a hydrodynamic limit for the system of random walks. The statement of the hydrodynamic limit that we prove is non-standard in that the evolution of the asymptotic particle density is given by the solution of a random rather than a deterministic PDE. The randomness in the PDE comes from the fact that under the hydrodynamic scaling the effect of the environment does not ``average out'' and so the specific instance of the environment chosen actually matters.<br />
<br />
The proof of the hydrodynamic limit for the system of RWRE will be accomplished by coupling the system of RWRE with a simpler model of a system of particles in an environment of ``directed traps.'' This talk is based on joint work with Milton Jara.<br />
<br />
== Thursday, September 25, [http://math.colorado.edu/~seor3821/ Sean O'Rourke], [http://www.colorado.edu/math/ University of Colorado Boulder] ==<br />
<br />
Title: '''Singular values and vectors under random perturbation'''<br />
<br />
Abstract:<br />
Computing the singular values and singular vectors of a large matrix is a basic task in high dimensional data analysis with many applications in computer science and statistics. In practice, however, data is often perturbed by noise. A natural question is the following. How much does a small perturbation to the matrix change the singular values and vectors? <br />
<br />
Classical (deterministic) theorems, such as those by Davis-Kahan, Wedin, and Weyl, give tight estimates for the worst-case scenario. In this talk, I will consider the case when the perturbation is random. In this setting, better estimates can be achieved when our matrix has low rank. This talk is based on joint work with Van Vu and Ke Wang.<br />
<br />
== Thursday, October 2, [http://www.math.wisc.edu/~jyin/jun-yin.html Jun Yin], [http://www.math.wisc.edu/ UW-Madison] ==<br />
<br />
Title: '''Anisotropic local laws for random matrices'''<br />
<br />
Abstract:<br />
In this talk, we introduce a new method of deriving local laws of random matrices. As applications, we will show the local laws and some universality results on general sample covariance matrices: TXX^*T^* (where $T$ is non-square deterministic matrix), and deformed Wigner matrix: H+A (where A is deterministic symmetric matrix). Note: here $TT^*$ and $A$ could be full rank matrices.<br />
<br />
== Thursday, October 9, No seminar due to [http://www.math.northwestern.edu/mwp/ Midwest Probability Colloquium] ==<br />
<br />
No seminar due to [http://www.math.northwestern.edu/mwp/ Midwest Probability Colloquium].<br />
<br />
<br />
== Thursday, October 16, TBA ==<br />
<br />
Title: TBA<br />
<br />
Abstract:<br />
<br />
<!-- == Thursday, October 23, TBA ==<br />
<br />
Title: TBA<br />
<br />
Abstract:<br />
--><br />
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<!-- == Thursday, October 30, TBA ==<br />
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Title: TBA<br />
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Abstract:<br />
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--><br />
<br />
== Thursday, November 6, Vadim Gorin, [http://www-math.mit.edu/people/profile.php?pid=1415 MIT] ==<br />
<br />
Title: TBA<br />
<br />
Abstract:<br />
<br />
== Friday, November 7, [http://tchumley.public.iastate.edu/ Tim Chumley], [http://www.math.iastate.edu/ Iowa State University] ==<br />
<br />
Title: TBA<br />
<br />
Abstract:<br />
<br />
== Thursday, November 13, TBA ==<br />
<br />
Title: TBA<br />
<br />
Abstract:<br />
<br />
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<!--<br />
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== Thursday, November 20, TBA ==<br />
<br />
Title: TBA<br />
<br />
Abstract:<br />
<br />
--><br />
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== ==<br />
<br />
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<br />
[[Past Seminars]]</div>Adminhttps://www.math.wisc.edu/wiki/index.php?title=NTS/Abstracts&diff=7946NTS/Abstracts2014-08-12T19:07:14Z<p>Admin: </p>
<hr />
<div>== January 23 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Majid Hadian-Jazi''' (UIC)<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: On a motivic method in Diophantine geometry<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: By studying the variation of motivic path torsors associated to a variety, we show how certain nondensity assertions in Diophantine geometry can be translated to problems concerning K-groups. Then we use some vanishing theorems to obtain concrete results.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== January 30 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Alexander Fish''' (University of Sydney, Australia)<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Ergodic Plunnecke inequalities with applications to sumsets of infinite sets in countable abelian groups<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: By use of recent ideas of Petridis, we extend Plunnecke inequalities for sumsets of finite sets in abelian groups to the setting of measure-preserving systems. The main difference in the new setting is that instead of a finite set of translates we have an analogous inequality for a countable set of translates. As an application, by use of Furstenberg correspondence principle, we obtain new Plunnecke type inequalities for lower and upper Banach density in countable abelian groups. Joint work with Michael Bjorklund, Chalmers. <br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== February 13 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''John Voight''' (Dartmouth)<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Numerical calculation of three-point branched covers of the projective line<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: We exhibit a numerical method to compute three-point branched covers of the complex projective line. We develop algorithms for working explicitly with Fuchsian triangle groups and their finite index subgroups, and we use these algorithms to compute power series expansions of modular forms on these groups. This is joint work with Michael Klug, Michael Musty, and Sam Schiavone.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== February 20 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Nir Avni''' (Northwestern)<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Representation zeta functions<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: I will talk about connections between the following:<br />
1) Asymptotic representation theory of an arithmetic lattice ''G''('''Z'''). More precisely, the question of how many ''n''-dimensional representations does ''G''('''Z''') have.<br />
2) The distribution of a random commutator in the ''p''-adic analytic group ''G''('''Z'''<sub>''p''</sub>).<br />
3) The complex geometry of the moduli spaces of ''G''-local systems on a Riemann surface, and, more precisely, the structure of its singularities.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== February 27 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Jennifer Park''' (MIT)<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Effective Chabauty for symmetric power of curves<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: While we know by Faltings' theorem that curves of genus at least 2 have finitely many rational points, his theorem is not effective. In 1985, Coleman showed that Chabauty's method, which works when the Mordell-Weil rank of the Jacobian of the curve is small, can be used to give a good effective bound on the number of rational points of curves of genus g > 1. In this talk, we draw ideas from tropical geometry to show that we can also give an effective bound on the number of rational points of Sym^d(X) that are not parametrized by a projective space or a coset of an abelian variety, where X is a curve of genus g > d, when the Mordell-Weil rank of the Jacobian of the curve is at most g-d. <br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== March 11 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Yueke Hu''' (Madison)<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Local integrals of triple product ''L''-function and subconvexity bound<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: Venkatesh proposed a strategy to prove the subconvexity bound in the level aspect for triple product ''L''-function. With the integral representation of triple product ''L''-function, if one can get an upper bound for the global integral and a lower bound for the local integrals, then one can get an upper bound for the ''L''-function, which turns out to be a subconvexity bound. Such a subconvexity bound was obtained essentially for representations of square free level. I will talk about how to generalize this result to the case with higher ramifications as well as joint ramifications.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== April 10 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Kartik Prasanna''' (Michigan)<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Algebraic cycles and Rankin-Selberg L-functions<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: I will give a survey of a circle of results relating L-functions and algebraic cycles, starting with the Gross-Zagier formula and its various generalizations. This will lead naturally to a certain case of the Bloch-Beilinson conjecture which is closely related to Gross-Zagier but where one does not have a construction of the expected cycles. Finally, I will hint at a plausible construction of cycles in this "missing" case, which is joint work with A. Ichino, and explain what one can likely prove about them.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== April 17 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Davide Reduzzi''' (Chicago)<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Galois representations and torsion in the coherent cohomology of<br />
Hilbert modular varieties<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: Let ''F'' be a totally real number field, ''p'' a prime number<br />
(unramified in ''F''), and ''M'' the Hilbert modular variety for ''F'' of some level<br />
prime to ''p'', and defined over a finite field of characteristic ''p''. I will<br />
explain how exploiting the geometry of ''M'', and in particular the<br />
stratification induced by the partial Hasse invariants, one can attach<br />
Galois representations to Hecke eigen-classes occurring in the coherent<br />
cohomology of ''M''. This is a joint work with Matthew Emerton and Liang Xiao.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== April 24 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Arul Shankar''' (Harvard)<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: The average 5-Selmer rank of elliptic curves<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: We use geometry-of-numbers techniques to show that the average size of the 5-Selmer group of<br />
elliptic curves is equal to 6. From this, we deduce an upper bound on the average rank of elliptic curves.<br />
Then, by constructing families of elliptic curves with equidistributed root number we show that the average rank is<br />
less than 1. This is joint work with Manjul Bhargava.<br />
|} <br />
</center><br />
<br />
<br><br />
== May 8 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Melanie Matchett Wood''' (UW-Madison)<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Jacobians of Random Graphs and Cohen Lenstra heuristics<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: We will consider the question of the distribution of the Jacobians of random curves over finite fields. Over a finite field, given a curve, we can associate to it the (finite) group of<br />
degree 0 line bundles on the curve. This is the function field analog of the class group of a number field.<br />
We will discuss the relationship to the Cohen Lenstra heuristics for the distribution of class groups. If the curve is reducible, a natural quotient of the Jacobian is the group of components, and we will focus on this aspect. We are thus led to study Jacobians of random graphs, which go by many names (including the sandpile group and the critical group) as they have arisen in a wide variety of contexts. We discuss new work proving a conjecture of Payne that Jacobians of random graphs satisfy a modified Cohen-Lenstra type heuristic.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<!--<br />
== October 3 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Andrew Bridy''' (Madison)<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: The Artin–Mazur zeta function of a Lattes map in positive characteristic<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: The Artin–Mazur zeta function of a dynamical system is a generating function that captures information about its periodic points. In characteristic zero, the zeta function of a rational map from '''P'''<sup>1</sup> to '''P'''<sup>1</sup> is known to always be a rational function. In positive characteristic, the situation is much less clear. Lattes maps are rational maps on '''P'''<sup>1</sup> that are finite quotients of endomorphisms of elliptic curves, and they have many interesting dynamical properties related to the geometry and arithmetic of elliptic curves. I show that the zeta function of a separable Lattes map in positive characteristic is a transcendental function.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== October 10 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Bogdan Petrenko''' (Eastern Illinois University)<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Generating an algebra from the probabilistic standpoint<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: Let ''A'' be a ring whose additive group is free Abelian of finite<br />
rank. The topic of this talk is the following question: what is the<br />
probability that several random elements of ''A'' generate it as a ring? After<br />
making this question precise, I will show that it has an interesting<br />
answer which can be interpreted as a local-global principle. Some<br />
applications will be discussed. This talk will be based on my joint work<br />
with Rostyslav Kravchenko (University of Chicago) and Marcin Mazur<br />
(Binghamton University).<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== October 17 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Anthony Várilly-Alvarado''' (Rice)<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Arithmetic of del Pezzo surfaces of degree 4 and vertical Brauer groups<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: Del Pezzo surfaces X of degree 4 are smooth (complete) intersections of two quadrics in four-dimensional projective space. They are some of the simplest surfaces for which there can be cohomological obstructions to the existence of rational points, mediated by the Brauer group Br X of the surface. I will explain how to construct, for every non-trivial, non-constant element A of Br X, a rational genus-one fibration X -> P^1 such that A is "vertical" for this map. This implies, for example, that if there is a cohomological obstruction to the existence of a point on X, then there is a genus-one fibration X -> P^1 where none of the fibers are locally soluble, giving a concrete, geometric way of "seeing" a Brauer-Manin obstruction. The construction also gives a fast, practical algorithm for computing the Brauer group of X. Conjecturally, this gives a mechanical way of testing for the existence of rational points on these surfaces. This is joint work with Bianca Viray.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== October 24 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Paul Garrett''' (Minnesota)<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Spectra of pseudo-Laplacians on spaces of automorphic forms<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: Faddeev–Pavlov and Lax–Phillips observed that certain<br />
restrictions of the Laplacian to parts of automorphic continuous<br />
spectrum have discrete spectrum. Colin de Verdiere used this to prove<br />
meromorphic continuation of Eisenstein series, and proposed ways to<br />
exploit this idea to construct self-adjoint operators with spectra<br />
related to zeros of ''L''-functions. We show that simple forms of this<br />
construction produce at most very sparse spectra, due to<br />
incompatibility with pair correlations for zeros. Ways around some of<br />
the obstacles are sketched. (Joint with E. Bombieri.)<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== October 31 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Jerry Wang''' (Princeton)<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Pencils of quadrics and the arithmetic of hyperelliptic curves<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: In recent joint works with Manjul Bhargava and Benedict Gross, we showed that a positive proportion of hyperelliptic curves over '''Q''' of genus ''g'' have no points over any odd degree extension of '''Q'''. This is done by computing certain 2-Selmer averages and applying a result of Dokchitser–Dokchitser on the parity of the rank of the 2-Selmer groups in biquadratic twists. In this talk, we will see how arithmetic invariant theory and the geometric theory of pencils of quadrics are used to obtain the 2-Selmer averages.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== November 7 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''who?''' (where?)<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: tba<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: tba<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== November 12 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Evan Dummit''' (Madison)<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Counting extensions of number fields of given degree, bounded (rho)-discriminant, and specified Galois closure<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: A very basic question in algebraic number theory is: how many number fields are there? A natural way to order the fields of a fixed degree n is by discriminant, and classical results of Minkowski then assure us that there are only finitely many fields with a given discriminant. We are also often interested in counting number fields, or relative extensions, with other properties, such as having a particular Galois closure. A folk conjecture sometimes attributed to Linnik states that the number of extensions of degree n and absolute discriminant less than X is on the order of X. A great deal of recent and ongoing work has been focused towards achieving upper bounds on counts of this nature (quite successfully, in degree 5 and lower), but there is comparatively little known in higher degrees, for relative extensions, or for sufficiently complicated Galois closures: the primary results are those of Schmidt and Ellenberg-Venkatesh. I will discuss these results and my thesis work, in which I generalize several of their results and introduce another counting metric, the "rho-discriminant". <br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== November 21 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Michael Lipnowski''' (Duke)<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: tba<br />
|-<br />
| bgcolor="#BCD2EE" |<br />
Abstract: tba<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== November 26 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Daniel Kane''' (Stanford)<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Diffuse decompositions of polynomials<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: We study some problems relating to polynomials evaluated<br />
either at random Gaussian or random Bernoulli inputs. We present some<br />
new work on a structure theorem for degree-''d'' polynomials with Gaussian<br />
inputs. In particular, if ''p'' is a given degree-''d'' polynomial, then ''p''<br />
can be written in terms of some bounded number of other polynomials<br />
''q''<sub>1</sub>, ..., ''q''<sub>''m''</sub> so that the joint probability density function of<br />
''q''<sub>1</sub>(''G''), ..., ''q''<sub>''m''</sub>(''G'') is close to being bounded. This says essentially<br />
that any abnormalities in the distribution of ''p''(''G'') can be explained by<br />
the way in which ''p'' decomposes into the ''q''<sub>''i''</sub>. We then present some<br />
applications of this result. <br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== December 5 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Jennifer Park''' (MIT)<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: tba<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: tba<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== December 12 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Vivek Shende''' (Berkeley)<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Equidistribution on the space of rank two vector bundles over the projective line<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: I will discuss how the algebraic geometry of hyperelliptic curves gives an approach to a function field analogue of the 'mixing conjecture' of Michel and Venkatesh. (For a rather longer abstract, see the [http://arxiv.org/abs/1307.8237 arxiv posting] of the same name as the talk). This talk presents joint work with Jacob Tsimerman. <br />
|} <br />
</center><br />
<br />
<br><br />
<br />
--><br />
<br />
== Organizer contact information ==<br />
<br />
[http://www.math.wisc.edu/~rharron/ Robert Harron]<br />
<br />
Sean Rostami<br />
<br />
----<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Adminhttps://www.math.wisc.edu/wiki/index.php?title=NTS/Abstracts&diff=7945NTS/Abstracts2014-08-12T19:06:50Z<p>Admin: Blanked the page</p>
<hr />
<div></div>Adminhttps://www.math.wisc.edu/wiki/index.php?title=Analysis&diff=2872Analysis2011-10-17T19:27:09Z<p>Admin: /* Postdocs */</p>
<hr />
<div>The members of the Analysis group work on a wide spectrum of topics. Research interests include:<br />
<br />
Complex Analysis, Harmonic Analysis, Partial Differential Equations, Mathematical Physics,<br />
Approximation Theory, Analysis on Lie groups, Wavelets, Analytic Number Theory, and <br />
Special Functions. <br />
<br />
<br />
==[http://www.math.wisc.edu/~seeger/curr.html Seminar]==<br />
The seminar will usually meet Tuesdays at 4:00 p.m., in B139 Van Vleck Hall.<br />
<br />
<br />
==[http://www.math.wisc.edu/~seeger/pastsem.html Past Seminars]==<br />
<br />
==[http://www.math.wisc.edu/~seeger/pastconf.html Conferences and other events]==<br />
<br />
[http://www.math.wisc.edu/~kiselev/conference2011.html Madison Springtime Analysis and PDE Workshop]<br />
April 30-May 1, 2011<br />
<br />
=='''Faculty'''==<br />
<br />
[[Image:Denissov.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~denissov Serguei Denissov]<br><br />
Moscow State University, 1999 <br><br />
Associate Professor<br><br />
denissov at math.wisc.edu<br />
<br />
[[Image:Gong.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~gong Xianghong Gong]<br><br />
University of Chicago, 1994<br><br />
Professor<br><br />
gong at math.wisc.edu<br />
<br />
[[Image:Kiselev.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~kiselev Alexander Kiselev]<br><br />
Caltech, 1996<br><br />
Professor<br><br />
kiselev at math.wisc.edu<br />
<br />
[[Image:anagel1.jpg|left|x110px|top]]<br />
http://www.math.wisc.edu/~nagel Alexander Nagel]<br><br />
Columbia, 1971<br><br />
Professor<br><br />
nagel at math.wisc.edu<br />
<br />
[[Image:Nazarov.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~nazarov Fëdor Nazarov]<br><br />
St. Petersburg State University, 1993<br><br />
Professor<br><br />
nazarov at math.wisc.edu<br />
<br />
[[Image:Amos_Ron.jpg|left|x110px|top]]<br />
[http://www.cs.wisc.edu/~amos Amos Ron]<br><br />
Tel Aviv University, 1987<br />
Professor<br><br />
amos at cs.wisc.edu<br />
<br />
[[Image:Seeger.jpg|left|x110px|top]] <br />
[http://www.math.wisc.edu/~seeger Andreas Seeger]<br><br />
Technical University, Darmstadt, 1985<br><br />
Professor<br><br />
seeger at math.wisc.edu<br />
<br />
[[Image:Street.jpg|left|x110px|top]] <br />
[http://www.math.wisc.edu/~street Brian Street]<br><br />
Princeton University, 2007<br><br />
Van Vleck Assistant Professor<br><br />
street at math.wisc.edu<br />
<br />
[[Image:Zlatos.jpg|left|x110px|top]]<br />
Andrej Zlatoš<br><br />
Caltech, 2003<br><br />
Assistant Professor<br><br />
zlatos at math.wisc.edu<br />
<br />
=='''Postdocs'''==<br />
<br />
[[Image:Fish.jpg|left|x110px|top]] <br />
[http://www.math.wisc.edu/~afish Alexander Fish]<br><br />
Hebrew University of Jerusalem, Israel, 2007<br><br />
Van Vleck Assistant Professor<br><br />
afish at math.wisc.edu<br />
<br />
[[Image:LaVictoire.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~patlavic Patrick LaVictoire]<br><br />
University of California (Berkeley), 2010 <br><br />
Van Vleck Assistant Professor<br><br />
patlavic at math.wisc.edu<br />
<br />
=='''[[Emeriti]]'''==<br />
<br />
[[Image:Wainger.jpg|left|x100px|top]]<br />
Stephen Wainger<br><br />
University of Chicago, 1961<br><br />
Professor<br><br />
wainger at math.wisc.edu<br />
<br />
=='''[[Former Members]]'''==<br />
<br />
[[Image:Ionescu.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~ionescu Alexandru Ionescu]<br><br />
Princeton, 1999<br><br />
Professor<br><br />
ionescu at math.princeton.edu</div>Adminhttps://www.math.wisc.edu/wiki/index.php?title=Analysis&diff=2871Analysis2011-10-17T19:26:29Z<p>Admin: /* Postdocs */</p>
<hr />
<div>The members of the Analysis group work on a wide spectrum of topics. Research interests include:<br />
<br />
Complex Analysis, Harmonic Analysis, Partial Differential Equations, Mathematical Physics,<br />
Approximation Theory, Analysis on Lie groups, Wavelets, Analytic Number Theory, and <br />
Special Functions. <br />
<br />
<br />
==[http://www.math.wisc.edu/~seeger/curr.html Seminar]==<br />
The seminar will usually meet Tuesdays at 4:00 p.m., in B139 Van Vleck Hall.<br />
<br />
<br />
==[http://www.math.wisc.edu/~seeger/pastsem.html Past Seminars]==<br />
<br />
==[http://www.math.wisc.edu/~seeger/pastconf.html Conferences and other events]==<br />
<br />
[http://www.math.wisc.edu/~kiselev/conference2011.html Madison Springtime Analysis and PDE Workshop]<br />
April 30-May 1, 2011<br />
<br />
=='''Faculty'''==<br />
<br />
[[Image:Denissov.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~denissov Serguei Denissov]<br><br />
Moscow State University, 1999 <br><br />
Associate Professor<br><br />
denissov at math.wisc.edu<br />
<br />
[[Image:Gong.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~gong Xianghong Gong]<br><br />
University of Chicago, 1994<br><br />
Professor<br><br />
gong at math.wisc.edu<br />
<br />
[[Image:Kiselev.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~kiselev Alexander Kiselev]<br><br />
Caltech, 1996<br><br />
Professor<br><br />
kiselev at math.wisc.edu<br />
<br />
[[Image:anagel1.jpg|left|x110px|top]]<br />
http://www.math.wisc.edu/~nagel Alexander Nagel]<br><br />
Columbia, 1971<br><br />
Professor<br><br />
nagel at math.wisc.edu<br />
<br />
[[Image:Nazarov.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~nazarov Fëdor Nazarov]<br><br />
St. Petersburg State University, 1993<br><br />
Professor<br><br />
nazarov at math.wisc.edu<br />
<br />
[[Image:Amos_Ron.jpg|left|x110px|top]]<br />
[http://www.cs.wisc.edu/~amos Amos Ron]<br><br />
Tel Aviv University, 1987<br />
Professor<br><br />
amos at cs.wisc.edu<br />
<br />
[[Image:Seeger.jpg|left|x110px|top]] <br />
[http://www.math.wisc.edu/~seeger Andreas Seeger]<br><br />
Technical University, Darmstadt, 1985<br><br />
Professor<br><br />
seeger at math.wisc.edu<br />
<br />
[[Image:Street.jpg|left|x110px|top]] <br />
[http://www.math.wisc.edu/~street Brian Street]<br><br />
Princeton University, 2007<br><br />
Van Vleck Assistant Professor<br><br />
street at math.wisc.edu<br />
<br />
[[Image:Zlatos.jpg|left|x110px|top]]<br />
Andrej Zlatoš<br><br />
Caltech, 2003<br><br />
Assistant Professor<br><br />
zlatos at math.wisc.edu<br />
<br />
=='''Postdocs'''==<br />
<br />
[[Image:Fish.jpg|left|x110px|top]] <br />
[http://www.math.wisc.edu/~afish Alexander Fish]<br><br />
Hebrew University of Jerusalem, Israel, 2007<br><br />
Van Vleck Assistant Professor<br><br />
afish at math.wisc.edu<br />
<br />
[[Image:LaVictoire.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~patlavic Patrick LaVictoire]<br><br />
University of California (Berkeley), 2010 <br><br />
Van Vleck Assistant Professor<br><br />
patlavic at math.wisc.edu<br />
<br />
[[Image:Street.jpg|left|x110px|top]] <br />
[http://www.math.wisc.edu/~street Brian Street]<br><br />
Princeton University, 2007<br><br />
Van Vleck Assistant Professor<br><br />
street at math.wisc.edu<br />
<br />
=='''[[Emeriti]]'''==<br />
<br />
[[Image:Wainger.jpg|left|x100px|top]]<br />
Stephen Wainger<br><br />
University of Chicago, 1961<br><br />
Professor<br><br />
wainger at math.wisc.edu<br />
<br />
=='''[[Former Members]]'''==<br />
<br />
[[Image:Ionescu.jpg|left|x110px|top]]<br />
[http://www.math.wisc.edu/~ionescu Alexandru Ionescu]<br><br />
Princeton, 1999<br><br />
Professor<br><br />
ionescu at math.princeton.edu</div>Adminhttps://www.math.wisc.edu/wiki/index.php?title=Main_Page&diff=76Main Page2010-01-11T23:43:56Z<p>Admin: </p>
<hr />
<div><br />
== Welcome to the University of Wisconsin Math Department Wiki ==<br />
<br />
This site is by and for the faculty, students and staff of the UW Mathematics Department. It contains useful information about the department, not always available from other sources. Pages can only be edited by members of the department but are viewable by everyone.<br />
<br />
== Getting started ==<br />
<br />
Consult the [http://meta.wikimedia.org/wiki/Help:Contents User's Guide] for information on using the wiki software.<br />
* [http://www.mediawiki.org/wiki/Manual:Configuration_settings Configuration settings list]<br />
* [http://www.mediawiki.org/wiki/Manual:FAQ MediaWiki FAQ]<br />
* [http://lists.wikimedia.org/mailman/listinfo/mediawiki-announce MediaWiki release mailing list]</div>Adminhttps://www.math.wisc.edu/wiki/index.php?title=UW-Math_Wiki:Community_Portal&diff=5UW-Math Wiki:Community Portal2010-01-08T19:26:52Z<p>Admin: New page: === Computer Help ===</p>
<hr />
<div>=== Computer Help ===</div>Adminhttps://www.math.wisc.edu/wiki/index.php?title=Main_Page&diff=4Main Page2010-01-08T19:25:50Z<p>Admin: /* Welcome to the University of Wisconsin Math Department Wiki */</p>
<hr />
<div><big>'''MediaWiki has been successfully installed.'''</big><br />
<br />
Consult the [http://meta.wikimedia.org/wiki/Help:Contents User's Guide] for information on using the wiki software.<br />
<br />
== Welcome to the University of Wisconsin Math Department Wiki ==<br />
<br />
This site is by and for the faculty, students and staff of the UW Mathematics Department. It contains useful information about the department, not always available from other sources. Pages can only be edited by members of the department but are viewable by everyone.<br />
<br />
== Getting started ==<br />
<br />
* [http://www.mediawiki.org/wiki/Manual:Configuration_settings Configuration settings list]<br />
* [http://www.mediawiki.org/wiki/Manual:FAQ MediaWiki FAQ]<br />
* [http://lists.wikimedia.org/mailman/listinfo/mediawiki-announce MediaWiki release mailing list]</div>Adminhttps://www.math.wisc.edu/wiki/index.php?title=Main_Page&diff=3Main Page2010-01-08T19:24:33Z<p>Admin: /* Welcome to the University of Wisconsin Math Department Wiki */</p>
<hr />
<div><big>'''MediaWiki has been successfully installed.'''</big><br />
<br />
Consult the [http://meta.wikimedia.org/wiki/Help:Contents User's Guide] for information on using the wiki software.<br />
<br />
== Welcome to the University of Wisconsin Math Department Wiki ==<br />
<br />
This site is by and for the faculty, students and staff of the UW Mathematics Department. It contains useful information about the department, not always available from other sources.<br />
<br />
== Getting started ==<br />
<br />
* [http://www.mediawiki.org/wiki/Manual:Configuration_settings Configuration settings list]<br />
* [http://www.mediawiki.org/wiki/Manual:FAQ MediaWiki FAQ]<br />
* [http://lists.wikimedia.org/mailman/listinfo/mediawiki-announce MediaWiki release mailing list]</div>Adminhttps://www.math.wisc.edu/wiki/index.php?title=Main_Page&diff=2Main Page2010-01-08T19:21:30Z<p>Admin: /* Getting started */</p>
<hr />
<div><big>'''MediaWiki has been successfully installed.'''</big><br />
<br />
Consult the [http://meta.wikimedia.org/wiki/Help:Contents User's Guide] for information on using the wiki software.<br />
<br />
== Welcome to the University of Wisconsin Math Department Wiki ==<br />
== Getting started ==<br />
<br />
* [http://www.mediawiki.org/wiki/Manual:Configuration_settings Configuration settings list]<br />
* [http://www.mediawiki.org/wiki/Manual:FAQ MediaWiki FAQ]<br />
* [http://lists.wikimedia.org/mailman/listinfo/mediawiki-announce MediaWiki release mailing list]</div>Admin