https://www.math.wisc.edu/wiki/api.php?action=feedcontributions&user=Nguyen34&feedformat=atomUW-Math Wiki - User contributions [en]2020-09-19T20:28:52ZUser contributionsMediaWiki 1.30.1https://www.math.wisc.edu/wiki/index.php?title=Past_Probability_Seminars_Spring_2020&diff=18455Past Probability Seminars Spring 20202019-11-20T15:17:03Z<p>Nguyen34: /* November 21, 2019, Tung Nguyen, UW Madison */</p>
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<div>__NOTOC__<br />
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= Fall 2019 =<br />
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<b>Thursdays in 901 Van Vleck Hall at 2:30 PM</b>, unless otherwise noted. <br />
<b>We usually end for questions at 3:20 PM.</b><br />
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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 />
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== September 12, 2019, [https://perso.univ-rennes1.fr/victor.kleptsyn/ Victor Kleptsyn], CNRS and University of Rennes 1 ==<br />
'''Furstenberg theorem: now with a parameter!'''<br />
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The classical Furstenberg theorem describes the (almost sure) behaviour of a random product of independent matrices; their norms turn out to grow exponentially. In our joint work with A. Gorodetski, we study what happens if the random matrices depend on an additional parameter. <br />
It turns out that in this new situation, the conclusion changes. Namely, under some conditions, there almost surely exists a (random) "exceptional" set on parameters where the lower limit for the Lyapunov exponent vanishes.<br />
Our results are related to the Anderson localization in dimension one, providing a purely dynamical viewpoint on its proof. I will also speak about some generalizations and related open questions.<br />
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== September 19, 2019, [http://math.columbia.edu/~xuanw Xuan Wu], Columbia University==<br />
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'''A Gibbs resampling method for discrete log-gamma line ensemble.'''<br />
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In this talk we will construct the discrete log-gamma line ensemble, which is assocaited with inverse gamma polymer model. This log-gamma line ensemble enjoys a random walk Gibbs resampling invariance that follows from the integrable nature of the inverse gamma polymer model via geometric RSK correspondance. By exploiting such resampling invariance, we show the tightness of this log-gamma line ensemble under weak noise scaling. Furthermore, a Gibbs property, as enjoyed by KPZ line ensemble, holds for all subsequential limits.<br />
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== October 10, 2019, NO SEMINAR - [https://sites.math.northwestern.edu/mwp/ Midwest Probability Colloquium] ==<br />
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== October 17, 2019, [https://www.usna.edu/Users/math/hottovy/index.php Scott Hottovy], USNA ==<br />
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''' Simplified dynamics for noisy systems with delays.'''<br />
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Many biological and physical systems include some type of random noise with a temporal delay. For example, many sperm cells travel in a random motion where their velocity changes according to a chemical signal. This chemotaxis is transmitted through a delay in the system. That is, the sperm notices chemical gradients after a certain time has elapsed. In this case, the delay causes the sperm to aggregate around the egg. In this talk I will consider a general stochastic differential delay equation (SDDE) with state-dependent colored noises and derive its limit as the time delays and the correlation times of the noises go to zero. The analysis leads to a much simpler Stochastic Differential Equation to study. The work is motivated by an experiment involving an electrical circuit with noisy, delayed feedback. The main methods used in the proof are a theorem about convergence of solutions of stochastic differential equations by Kurtz and Protter and a maximal inequality for sums of a stationary sequence of random variables by Peligrad and Utev.<br />
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== October 24, 2019, [https://math.temple.edu/~brider/ Brian Rider], Temple University ==<br />
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'''A general beta crossover ensemble'''<br />
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I'll describe an operator limit for a family of general beta ensembles which exhibit a double-scaling. In particular, a free parameter in the system provides for a crossover between the more well-known "soft" and "hard" edge point processes. This new limit operator takes as input the Riccati diffusion associated with the Stochastic Airy Operator. I like to suggest that this hints at a hierarchy of random operators analogous to the Painlevé hierarchy observed at the level of correlation functions for double-scaling ensembles most widely studied at beta = 2. Full disclosure: the result remains partially conjectural due to an unresolved uniqueness question, but I’ll provide lots of evidence to convince you we have the right answer. Joint work with Jose Ramírez (Univ. Costa Rica).<br />
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== October 31, 2019, Vadim Gorin, UW Madison==<br />
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'''Shift invariance for the six-vertex model and directed polymers.'''<br />
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I will explain a recently discovered mysterious property in a variety of stochastic systems ranging from the six-vertex model and to the directed polymers, last passage percolation, Kardar-Parisi-Zhang equation, and Airy sheet. Vaguely speaking, the property says that the multi-point joint distributions are unchanged when some (but not necessarily all!) points of observations are shifted. The property leads to explicit computations for the previously inaccessible joint distributions in all these settings.<br />
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== November 7, 2019, [https://people.kth.se/~tobergg/ Tomas Berggren], KTH Stockholm ==<br />
'''Domino tilings of the Aztec diamond with doubly periodic weightings'''<br />
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This talk will be centered around domino tilings of the Aztec diamond with doubly periodic weightings. In particular asymptotic results of the $ 2 \times k $-periodic Aztec diamond will be discussed, both in the macroscopic and microscopic scale. The macroscopic picture is described using a close connection to a Riemann surface. For instance, the number of smooth regions (also called gas regions) is the same as the genus of the mentioned Riemann surface. <br />
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The starting point of the asymptotic analysis is a non-intersecting path formulation and a double integral formula for the correlation kernel. The proof of this double integral formula is based on joint work with M. Duits, which will be discuss briefly if time permits.<br />
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== November 14, 2019, [https://math.mit.edu/directory/profile.php?pid=2076 Benjamin Landon], MIT ==<br />
'''Universality of extremal eigenvalue statistics of random matrices'''<br />
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The past decade has seen significant progress on the understanding of universality of various eigenvalue statistics of random matrix theory. However, the behavior of certain ``extremal'' or ``critical'' observables is not fully understood. Towards the former, we discuss progress on the universality of the largest gap between consecutive eigenvalues. With regards to the latter, we discuss the central limit theorem for the eigenvalue counting function, which can be viewed as a linear spectral statistic with critical regularity and has logarithmically growing variance.<br />
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== November 21, 2019, Tung Nguyen, UW Madison ==<br />
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'''Prevalence of deficiency zero reaction networks under an Erdos-Renyi framework<br />
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Reaction network models, which are used to model many types of systems in biology, have grown dramatically in popularity over the past decade. This popularity has translated into a number of mathematical results that relate the topological features of the network to different qualitative behaviors of the associated dynamical system. One of the main topological features studied in the field is ''deficiency'' of a network. A reaction network which has strong connectivity in its connected components and a deficiency of zero is stable in both the deterministic and stochastic dynamical models.<br />
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This leads to the question: how prevalent are deficiency zero models among all such network models. In this talk, I will quantify the prevalence of deficiency zero networks among random reaction networks generated under an Erdos-Renyi framework. Specifically, with n being the number of species, I will uncover a threshold function r(n) such that the probability of the random network being deficiency zero converges to 1 if the edge probability p_n << r(n) and converges to 0 if p_n >> r(n).<br />
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== November 28, 2019, Thanksgiving (no seminar) ==<br />
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==December 5, 2019 ==<br />
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[[Past Seminars]]</div>Nguyen34https://www.math.wisc.edu/wiki/index.php?title=AMS_Student_Chapter_Seminar&diff=18290AMS Student Chapter Seminar2019-11-01T23:08:39Z<p>Nguyen34: /* November 6, Tung Nguyen */</p>
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<div>The AMS Student Chapter Seminar is an informal, graduate student seminar on a wide range of mathematical topics. Pastries (usually donuts) will be provided.<br />
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* '''When:''' Wednesdays, 3:20 PM – 3:50 PM<br />
* '''Where:''' Van Vleck, 9th floor lounge (unless otherwise announced)<br />
* '''Organizers:''' [https://www.math.wisc.edu/~malexis/ Michel Alexis], [https://www.math.wisc.edu/~drwagner/ David Wagner], [http://www.math.wisc.edu/~nicodemus/ Patrick Nicodemus], [http://www.math.wisc.edu/~thaison/ Son Tu], Carrie Chen<br />
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Everyone is welcome to give a talk. To sign up, please contact one of the organizers with a title and abstract. Talks are 30 minutes long and should avoid assuming significant mathematical background beyond first-year graduate courses.<br />
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The schedule of talks from past semesters can be found [[AMS Student Chapter Seminar, previous semesters|here]].<br />
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== Fall 2019 ==<br />
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=== October 9, Brandon Boggess===<br />
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Title: An Application of Elliptic Curves to the Theory of Internet Memes<br />
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Abstract: Solve polynomial equations with this one weird trick! Math teachers hate him!!!<br />
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[[File:Thumbnail fruit meme.png]]<br />
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=== October 16, Jiaxin Jin===<br />
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Title: Persistence and global stability for biochemical reaction-diffusion systems<br />
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Abstract: The investigation of the dynamics of solutions of nonlinear reaction-diffusion PDE systems generated by biochemical networks is a great challenge; in general, even the existence of classical solutions is difficult to establish. On the other hand, these kinds of problems appear very often in biological applications, e.g., when trying to understand the role of spatial inhomogeneities in living cells. We discuss the persistence and global stability properties of special classes of such systems, under additional assumptions such as: low number of species, complex balance or weak reversibility.<br />
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=== October 23, Erika Pirnes===<br />
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(special edition: carrot seminar)<br />
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Title: Why do ice hockey players fall in love with mathematicians? (Behavior of certain number string sequences)<br />
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Abstract: Starting with some string of digits 0-9, add the adjacent numbers pairwise to obtain a new string. Whenever the sum is 10 or greater, separate its digits. For example, 26621 would become 81283 and then 931011. Repeating this process with different inputs gives varying behavior. In some cases the process terminates (becomes a single digit), or ends up in a loop, like 999, 1818, 999... The length of the strings can also start growing very fast. I'll discuss some data and conjectures about classifying the behavior.<br />
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=== October 30, Yunbai Cao===<br />
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Title: Kinetic theory in bounded domains<br />
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Abstract: In 1900, David Hilbert outlined 23 important problems in the International Congress of Mathematics. One of them is the Hilbert's sixth problem which asks the mathematical linkage between the mechanics from microscopic view and the macroscopic view. A relative new mesoscopic point of view at that time which is "kinetic theory" was highlighted by Hilbert as the bridge to link the two. In this talk, I will talk about the history and basic elements of kinetic theory and Boltzmann equation, and the role boundary plays for such a system, as well as briefly mention some recent progress.<br />
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=== November 6, Tung Nguyen===<br />
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Title: Introduction to Chemical Reaction Network<br />
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Abstract: Reaction network models are often used to investigate the dynamics of different species from various branches of chemistry, biology and ecology. The study of reaction network has grown significantly and involves a wide range of mathematics and applications. In this talk, I aim to show a big picture of what is happening in reaction network theory. I will first introduce the basic dynamical models for reaction network: the deterministic and stochastic models. Then, I will mention some big questions of interest, and the mathematical tools that are used by people in the field. Finally, I will make connection between reaction network and other branches of mathematics such as PDE, control theory, and random graph theory.<br />
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=== November 13, Stephen Davis===<br />
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Title: Random Motion<br />
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Abstract: We'll talk about how to see random motions from different points of view. We'll end up placing one of our favorite random motions in a very creative geometric space, which will help us see things we couldn't see before.<br />
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=== November 20, Colin Crowley===<br />
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Title: TBD<br />
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Abstract: TBD<br />
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=== December 4, Xiaocheng Li===<br />
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Title: TBD<br />
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Abstract: TBD<br />
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=== December 11, Chaojie Yuan===<br />
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Title: TBD<br />
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Abstract: TBD</div>Nguyen34