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__NOTOC__
= Mathematics Colloquium =
= Mathematics Colloquium =


All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.


<!-- ==[[Tentative Colloquia|Tentative schedule for next semester]] == -->
The calendar for spring 2019 can be found [[Colloquia/Spring2019|here]].
 
== Fall 2018 ==


== Fall 2016  ==
 
{| cellpadding="8"
!align="left" | date 
!align="left" | speaker
!align="left" | title
!align="left" | host(s)
|-
|September 9
|
|[[#  |    ]]
|
|
|-
|September 16
|[http://www.math.cmu.edu/~ploh/ Po-Shen Loh] (CMU)
|Directed paths: from Ramsey to Pseudorandomness
|Ellenberg
|
|-
|September 23
| [http://www.math.wisc.edu/~craciun/ Gheorghe Craciun] (UW-Madison)
|Toric Differential Inclusions and a Proof of the Global Attractor Conjecture
| Street
|[[#  |    ]]
|-
|September 30
|[http://math.uga.edu/~magyar/ Akos Magyar]  (University of Georgia)
|Geometric Ramsey theory
| Cook
|
|-
|October 7
|
|[[# |    ]]
|
|
|-
|October 14
|  [https://www.math.lsu.edu/~llong/ Ling Long] (LSU)
|Hypergeometric functions over finite fields
| Yang
|
|-
|October 21
|'''No colloquium this week'''
|[[#  |    ]]
|
|
|-
|'''Tuesday, October 25, 9th floor'''
|[http://users.math.yale.edu/users/steinerberger/ Stefan Steinerberger] (Yale)
|Three Miracles in Analysis
|Seeger
|
|-
|October 28, 9th floor
|  [http://order.ph.utexas.edu/people/Reichl.htm Linda Reichl] (UT Austin)
|Microscopic hydrodynamic modes in a binary mixture
|Minh-Binh Tran
|
|-
|'''Monday, October 31, B239'''
|  [https://math.berkeley.edu/~kpmann/ Kathryn Mann] (Berkeley)
|Groups acting on the circle
|Smith
|
|-
|November 4
|
|
|
|
|-
|'''Monday, November 7 at 4:30, 9th floor''' ([http://www.ams.org/meetings/lectures/maclaurin-lectures AMS Maclaurin lecture])
| [http://www.massey.ac.nz/massey/expertise/profile.cfm?stref=339830 Gaven Martin] (New Zealand Institute for Advanced Study)
|Siegel's problem on small volume lattices
| Marshall
|
|-
|November 11
|  Reserved for possible job talks
|[[# |    ]]
|
|
|-
|'''Wednesday, November 16, 9th floor'''
|  [http://math.uchicago.edu/~klindsey/ Kathryn Lindsey] (U Chicago)
|Shapes of Julia Sets
|Michell
|
|-
|November 18, B239
|[http://www-personal.umich.edu/~asnowden/ Andrew Snowden] (University of Michigan)
|Recent progress in representation stability
|Ellenberg
|
|-
|'''Monday, November 21, 9th floor'''
|[https://www.fmi.uni-sofia.bg/fmi/logic/msoskova/index.html Mariya Soskova] (University of Wisconsin-Madison)
|Definability in degree structures
|Smith
|
|-
|November 25
|  '''Thanksgiving break'''
|[[# |    ]]
|
|
|-
|December 2, 9th floor
|  [http://math.columbia.edu/~hshen/ Hao Shen] (Columbia)
|[[#Friday, December 2:  Hao Shen (Columbia) | ''Singular Stochastic Partial Differential Equations - How do they arise and what do they mean?'']]
|Roch
|
|-
|'''Monday, December 5, B239'''
|  [https://www.math.wisc.edu/~wang/ Botong Wang] (UW Madison)
|[[#Monday, December 5: Botong Wang  (UW-Madison) | ''Enumeration of points, lines, planes, etc.'']]
|Maxim
|
|-
|December 9, B239
|  [http://math.uchicago.edu/~awbrown/ Aaron Brown] (U Chicago)
| [[#Friday, December 9: Aaron Brown  (U Chicago) | ''Lattice actions and recent progress in the Zimmer program'']]
|Kent
|-
|'''Monday, December 19, B115'''
|  [http://math.uchicago.edu/~andrew.zimmer/ Andrew Zimmer] (U Chicago)
| Metric spaces of non-positive curvature and applications in several complex variables
|Gong
|}


== Spring 2017  ==
 
{| cellpadding="8"
{| cellpadding="8"
!align="left" | date   
!align="left" | date   
Line 150: Line 14:
!align="left" | host(s)
!align="left" | host(s)
|-
|-
|'''Monday, January 9, 9th floor'''
|Sep 12    '''Room 911'''
| [http://www.stat.berkeley.edu/~racz/ Miklos Racz] (Microsoft)
| [https://sites.math.washington.edu/~gunther/ Gunther Uhlmann] (Univ. of Washington) Distinguished Lecture series
|[[#Monday, January 9:  Miklos Racz (Microsoft) |  ''Statistical inference in networks and genomics''  ]]
|[[#Sep 12: Gunther Uhlmann (Univ. of Washington)|  Harry Potter's Cloak via Transformation Optics ]]
|  Valko
| Li
|
|-
|January 13, B239
|  [https://math.berkeley.edu/people/faculty/mihaela-ifrim/ Mihaela Ifrim] (Berkeley)
|[[#Friday, January 13: Mihaela Ifrim (Berkeley) |  ''Two dimensional water waves''  ]]
|  Angenent
|
|-
|January 20
|  [http://math.mit.edu/~sraskin/ Sam Raskin] (MIT)
|[[# TBA TBA  ]]
|  Arinkin
|
|-
|'''Monday, January 23'''
| [http://www.math.umd.edu/~tdarvas/ Tamas Darvas] (Maryland)
|[[# TBA |  TBA  ]]
|  Viaclovsky
|
|-
|January 27
|Reserved for possible job talks
|[[# |    ]]
|
|
|-
|-
|February 3
|Sep 14    '''Room 911'''
|
| [https://sites.math.washington.edu/~gunther/ Gunther Uhlmann] (Univ. of Washington) Distinguished Lecture series
|[[#   TBA|   TBA ]]
|[[#Sep 14: Gunther Uhlmann (Univ. of Washington) | Journey to the Center of the Earth ]]
|
| Li
|
|
|-
|-
|February 6 (Wasow lecture)
|Sep 21    '''Room 911'''
| Benoit Perthame (University of Paris VI)
| [http://stuart.caltech.edu/  Andrew Stuart] (Caltech) LAA lecture
|[[# TBATBA ]]  
|[[#Sep 21: Andrew Stuart (Caltech) The Legacy of Rudolph Kalman  ]]
| Jin
| Jin
|-
|February 10 (WIMAW lecture)
| Alina Chertock (NC State Univ.)
|[[# |  ]]
| WIMAW
|
|
|-
|-
|February 17
|Sep 28
| [http://web.math.ucsb.edu/~ponce/ Gustavo Ponce] (UCSB)
| [https://www.math.cmu.edu/~gautam/sj/index.html Gautam Iyer] (CMU)
|[[#   |     ]]
|[[#Sep 28: Gautam Iyer (CMU)| Stirring and Mixing ]]
| Minh-Binh Tran
| Thiffeault
|
|
|-
|-
|February 24
|Oct 5
|  
| [http://www.personal.psu.edu/eus25/ Eyal Subag] (Penn State)
|[[#  |    ]]
|[[#Oct 5: Eyal Subag (Penn State)|  Symmetries of the hydrogen atom and algebraic families ]]
|  
| Gurevich
|
|
|-
|-
|March 3
|Oct 12
| [http://www.math.utah.edu/~bromberg/ Ken Bromberg] (University of Utah)
| [https://www.math.wisc.edu/~andreic/ Andrei Caldararu] (Madison)
|[[# |   ]]
|[[#Oct 12: Andrei Caldararu (Madison) | Mirror symmetry and derived categories  ]]
|Dymarz
| ...
|
|
|-
|-
|Tuesday, March 7, 4PM (Distinguished Lecture)
|Oct 19
| [http://pages.iu.edu/~temam/  Roger Temam] (Indiana University)  
| [https://teitelbaum.math.uconn.edu/# Jeremy Teitelbaum] (U Connecticut)
|[[#  |    ]]
|[[#Oct 19:  Jeremy Teitelbaum (U Connecticut)|  Lessons Learned and New Perspectives: From Dean and Provost to aspiring Data Scientist ]]
|Smith
| Boston
|
|
|-
|-
|Wednesday, March 8, 2:25PM
|Oct 26
| [http://pages.iu.edu/~temam/ Roger Temam] (Indiana University)  
| [http://math.arizona.edu/~ulmer/index.html Douglas Ulmer] (Arizona)
|[[# |   ]]
|[[#Oct 26: Douglas Ulmer (Arizona) | Rational numbers, rational functions, and rational points ]]
|Smith
| Yang
|
|
|-
|-
|March 10
|Nov 2
| '''No Colloquium'''
| Reserved for job talk
|[[# |   ]]
|[[# TBA| TBA  ]]
|
| hosting faculty
|
|
|-
|-
|Wednesday, March 15, 4PM
|Nov 9
| [http://verso.mat.uam.es/web/ezuazua/zuazua.html Enrique Zuazua] (Universidad Autónoma de Madrid)
| Reserved for job talk
|[[#   TBA|   TBA  ]]
|[[# TBA| TBA  ]]
| Jin & Minh-Binh Tran
| hosting faculty
|
|
|-
|-
|March 17
|Nov 16
| [https://services.math.duke.edu/~pierce/ Lillian Pierce] (Duke University)
| Reserved for job talk
| TBA
|[[# TBA| TBA ]]
| M. Matchett Wood
| hosting faculty
|
|
|-
|-
|March 24
|Nov 30
| '''Spring Break'''
| Reserved for job talk
|[[# |   ]]
|[[# TBA| TBA  ]]
|
| hosting faculty
|
|
|-
|-
|Wednesday, March 29 (Wasow)
|Dec 7
| [https://math.nyu.edu/faculty/serfaty/ Sylvia Serfaty] (NYU)
| Reserved for job talk
|[[# TBA|   TBA]]
|[[# TBA| TBA  ]]
|Tran
| hosting faculty
|
|-
|March 31
| '''No Colloquium'''
|[[# |    ]]
|
|
|-
|April 7
| [http://www.math.uiuc.edu/~schenck/ Hal Schenck]
|[[# |    ]]
|Erman
|
|-
|April 14
| Wilfrid Gangbo
|[[# |    ]]
|Feldman & Tran
|
|
|-
|April 21
|  [http://www.math.stonybrook.edu/~mde/ Mark Andrea de Cataldo]  (Stony Brook)
|TBA
| Maxim
|
|-
|April 28
| [http://users.cms.caltech.edu/~hou/ Thomas Yizhao Hou] 
|[[# TBA|  TBA  ]]
|Li
|}
|}


== Abstracts ==
== Abstracts ==
=== September 16: Po-Shen Loh (CMU) ===
Title: Directed paths: from Ramsey to Pseudorandomness


Abstract: Starting from an innocent Ramsey-theoretic question regarding directed
=== Sep 12: Gunther Uhlmann (Univ. of Washington) ===
paths in graphs, we discover a series of rich and surprising connections
Harry Potter's Cloak via Transformation Optics
that lead into the theory around a fundamental result in Combinatorics:
Szemeredi's Regularity Lemma, which roughly states that every graph (no
matter how large) can be well-approximated by a bounded-complexity
pseudorandom object. Using these relationships, we prove that every
coloring of the edges of the transitive N-vertex tournament using three
colors contains a directed path of length at least sqrt(N) e^{log^* N}
which entirely avoids some color.  The unusual function log^* is the
inverse function of the tower function (iterated exponentiation).


=== September 23: Gheorghe Craciun (UW-Madison) ===
Can we make objects invisible? This has been a subject of human
Title: Toric Differential Inclusions and a Proof of the Global Attractor Conjecture
fascination for millennia in Greek mythology, movies, science fiction,
etc. including the legend of Perseus versus Medusa and the more recent
Star Trek and Harry Potter. In the last fifteen years or so there have been
several scientific proposals to achieve invisibility. We will introduce in a non-technical fashion
one of them, the so-called "traansformation optics"
in a non-technical fashion n the so-called that has received the most attention in the
scientific literature.


Abstract: The Global Attractor Conjecture says that a large class of polynomial dynamical systems, called toric dynamical systems, have a globally attracting point within each linear invariant space. In particular, these polynomial dynamical systems never exhibit multistability, oscillations or chaotic dynamics.
=== Sep 14: Gunther Uhlmann (Univ. of Washington) ===
Journey to the Center of the Earth


The conjecture was formulated by Fritz Horn in the early 1970s, and is strongly related to Boltzmann's H-theorem.
We will consider the inverse problem of determining the sound
speed or index of refraction of a medium by measuring the travel times of
waves going through the medium. This problem arises in global seismology
in an attempt to determine the inner structure of the Earth by measuring
travel times of earthquakes. It has also several applications in optics
and medical imaging among others.


We discuss the history of this problem, including the connection between this conjecture and the Boltzmann equation. Then, we introduce toric differential inclusions, and describe how they can be used to prove this conjecture in full generality.  
The problem can be recast as a geometric problem: Can one determine the
Riemannian metric of a Riemannian manifold with boundary by measuring
the distance function between boundary points? This is the boundary
rigidity problem. We will also consider the problem of determining
the metric from the scattering relation, the so-called lens rigidity
problem. The linearization of these problems involve the integration
of a tensor along geodesics, similar to the X-ray transform.


=== September 30: Akos Magyar (University of Georgia) ===
We will also describe some recent results, join with Plamen Stefanov
Title: Geometric Ramsey theory
and Andras Vasy, on the partial data case, where you are making
measurements on a subset of the boundary. No previous knowledge of
Riemannian geometry will be assumed.


Abstract: Initiated by Erdos, Graham, Montgomery and others in the 1970's, geometric Ramsey theory studies geometric configurations, determined up to translations, rotations and possibly dilations, which cannot be destroyed by finite partitions of Euclidean spaces. Later it was shown by ergodic and Fourier analytic methods that such results are also possible in the context of sets of positive upper density in Euclidean spaces or the integer lattice. We present a new approach, motivated by developments in arithmetic combinatorics, which provide new results as well new proofs of some classical results in this area.
=== Sep 21: Andrew Stuart (Caltech) ===


=== October 14: Ling Long (LSU) ===
The Legacy of Rudolph Kalman
Title: Hypergeometric functions over finite fields


Abstract: Hypergeometric functions are special functions with lot of
In 1960 Rudolph Kalman published what is arguably the first paper to develop a systematic, principled approach to the use of data to improve the predictive capability of mathematical models. As our ability to gather data grows at an enormous rate, the importance of this work continues to grow too. The lecture will describe this paper, and developments that have stemmed from it, revolutionizing fields such space-craft control, weather prediction, oceanography and oil recovery, and with potential for use in new fields such as medical imaging and artificial intelligence. Some mathematical details will be also provided, but limited to simple concepts such as optimization, and iteration; the talk is designed to be broadly accessible to anyone with an interest in quantitative science.
symmetries. In this talk, we will introduce hypergeometric functions over finite
fields, originally due to Greene, Katz and McCarthy, in a way that is
parallel to the classical hypergeometric functions, and discuss their
properties and applications to character sums and the arithmetic of
hypergeometric abelian varieties.
This is a joint work with Jenny Fuselier, Ravi Ramakrishna, Holly Swisher, and Fang-Ting Tu.


=== Tuesday, October 25, 9th floor: Stefan Steinerberger (Yale) ===
=== Sep 28: Gautam Iyer (CMU) ===
Title: Three Miracles in Analysis


Abstract: I plan to tell three stories: all deal with new points of view on very classical objects and have in common that there is a miracle somewhere. Miracles are nice but difficult to reproduce, so in all three cases the full extent of the underlying theory is not clear and many interesting open problems await. (1) An improvement of the Poincare inequality on the Torus that encodes a lot of classical Number Theory. (2) If the Hardy-Littlewood maximal function is easy to compute, then the function is sin(x). (Here, the miracle is both in the statement and in the proof). (3) Bounding classical integral operators (Hilbert/Laplace/Fourier-transforms) in L^2 -- but this time from below (this problem originally arose in medical imaging). Here, the miracle is also known as 'Slepian's miracle' (this part is joint work with Rima Alaifari, Lillian Pierce and Roy Lederman).
Stirring and Mixing


=== October 28: Linda Reichl (UT Austin) ===
Mixing is something one encounters often in everyday life (e.g. stirring cream into coffee). I will talk about two mathematical
Title: Microscopic hydrodynamic modes in a binary mixture
aspects of mixing that arise in the context of fluid dynamics:


Abstract: Expressions for propagation speeds and decay rates of hydrodynamic modes in a binary mixture can be obtained directly from spectral properties of the Boltzmann equations describing the mixture. The derivation of hydrodynamic behavior from the spectral properties of the kinetic equation provides an alternative to Chapman-Enskog theory, and removes the need for lengthy calculations of transport coefficients in the mixture. It also provides a sensitive test of the completeness of kinetic equations describing the mixture. We apply the method to a hard-sphere binary mixture and show that it gives excellent agreement with light scattering experiments on noble gas mixtures.
1. How efficiently can stirring "mix"?


===Monday, October 31: Kathryn Mann (Berkeley) ===
2. What is the interaction between diffusion and mixing.
Title: Groups acting on the circle


Abstract:  Given a group G and a manifold M, can one describe all the actions of G on M?  This is a basic and natural question from geometric topology, but also a very difficult one -- even in the case where M is the circle, and G is a familiar, finitely generated group.
Both these aspects are rich in open problems whose resolution involves tools from various different areas. I present a brief survey of existing
results, and talk about a few open problems.


In this talk, I’ll introduce you to the theory of groups acting on the circle, building on the perspectives of Ghys, Calegari, Goldman and others.  We'll see some tools, old and new, some open problems, and some connections between this theory and themes in topology (like foliated bundles) and dynamics. 
=== Oct 5: Eyal Subag (Penn State)===


===November 7: Gaven Martin (New Zealand Institute for Advanced Study) ===
Symmetries of the hydrogen atom and algebraic families
Title: Siegel's problem on small volume lattices


Abstract: We outline in very general terms the history and the proof of the identification
The hydrogen atom system is one of the most thoroughly studied examples of a quantum mechanical system. It can be fully solved, and the main reason why is its (hidden) symmetryIn this talk I shall explain how the symmetries of the Schrödinger equation for the hydrogen atom, both visible and hidden, give rise to an example in the recently developed theory of algebraic families of Harish-Chandra modulesI will show how the algebraic structure of these symmetries completely determines the spectrum of the Schrödinger operator and sheds new light on the quantum nature of the system.  No prior knowledge on quantum mechanics or representation theory will be assumed.
of the minimal covolume lattice of hyperbolic 3-space as the 3-5-3
Coxeter group extended by the involution preserving the symmetry of this
diagram. This gives us the smallest regular tessellation of hyperbolic 3-space.
This solves (in three dimensions) a problem posed by Siegel in 1945Siegel solved this problem in two dimensions by deriving the
signature formula identifying the (2,3,7)-triangle group as having minimal
co-area.
   
There are strong connections with arithmetic hyperbolic geometry in
the proof, and the result has applications in the maximal symmetry groups
of hyperbolic 3-manifolds in much the same way that Hurwitz's 84g-84 theorem
and Siegel's result do.


===Wednesday, November 16 (9th floor): Kathryn Lindsey (U Chicago) ===
=== Oct 12: Andrei Caldararu (Madison)===
Title: Shapes of Julia Sets


Abstract: The filled Julia set of a complex polynomial P is the set of points whose orbit under iteration of the map P is bounded.  William Thurston asked "What are the possible shapes of polynomial Julia sets?"  For example, is there a polynomial whose Julia set looks like a cat, or your silhouette, or spells out your name?  It turns out the answer to all of these is "yes!"  I will characterize the shapes of polynomial Julia sets and present an algorithm for constructing polynomials whose Julia sets have desired shapes.
Mirror symmetry and derived categories


===November 18: Andrew Snowden (University of Michigan)===
Mirror symmetry is a remarkable phenomenon, first discovered in physics. It relates two seemingly disparate areas of mathematics, symplectic and algebraic geometry. Its initial formulation was rather narrow, as a technique for computing enumerative invariants (so-called Gromov-Witten invariants) of symplectic varieties by solving certain differential equations describing the variation of Hodge structure of “mirror" varieties. Over the past 25 years this narrow view has expanded considerably, largely due to insights of M. Kontsevich who introduced techniques from derived categories into the subject. Nowadays mirror symmetry encompasses wide areas of mathematics, touching on subjects like birational geometry, number theory, homological algebra, etc.
Title: Recent progress in representation stability


Abstract:  Representation stability is a relatively new field that studies
In my talk I shall survey some of the recent developments in mirror symmetry, and I will explain how my work fits in the general picture. In particular I will describe an example of derived equivalent but not birational Calabi-Yau three folds (joint work with Lev Borisov); and a recent computation of a categorical Gromov-Witten invariant of positive genus (work with my former student Junwu Tu).
somewhat exotic algebraic structures and exploits their properties to
prove results (often asymptotic in nature) about objects of interest.
I will describe some of the algebraic structures that appear (and
state some important results about them), give a sampling of some
notable applications (in group theory, topology, and algebraic
geometry), and mention some open problems in the area.


===Monday, November 21: Mariya Soskova (University of Wisconsin-Madison)===
=== Oct 19:   Jeremy Teitelbaum (U Connecticut)===
Title: Definability in degree structures
Lessons Learned and New Perspectives:
From Dean and Provost to aspiring Data Scientist


Abstract:  Some incomputable sets are more incomputable than others. We use
After more than 10 years in administration, including 9 as Dean of
Turing reducibility and enumeration reducibility to measure the
Arts and Sciences and 1 as interim Provost at UConn, I have returned
relative complexity of incomputable sets. By identifying sets of the
to my faculty position.  I am spending a year as a visiting scientist
same complexity, we can associate to each reducibility a degree
at the Jackson Laboratory for Genomic Medicine (JAX-GM) in Farmington,
structure: the partial order of the Turing degrees and the partial
Connecticut, trying to get a grip on some of the mathematical problems
order of the enumeration degrees. The two structures are related in
of interest to researchers in cancer genomics. In this talk, I will offer some personal
nontrivial ways. The first has an isomorphic copy in the second and
observations about being a mathematician and a high-level administrator, talk a bit about
this isomorphic copy is an automorphism base. In 1969, Rogers asked a
the research environment at an independent research institute like JAX-GM, outline
series of questions about the two degree structures with a common
a few problems that I've begun to learn about, and conclude with a
theme: definability. In this talk I will introduce the main concepts
discussion of how these experiences have shaped my view of graduate training in mathematics.
and describe the work that was motivated by these questions.


===Friday, December 2: Hao Shen (Columbia)===
=== Oct 26: Douglas Ulmer (Arizona)===
Title:  Singular Stochastic Partial Differential Equations - How do they arise and what do they mean?


Abstract: Systems with random fluctuations are ubiquitous in the real world. Stochastic PDEs are default models for these random systems, just as PDEs are default models for deterministic systems. However, a large class of such stochastic PDEs were poorly understood until very recently: the presence of very singular random forcing as well as nonlinearities render it challenging to interpret what one even means by a ``solution". The recent breakthroughs by M. Hairer, M. Gubinelli and other researchers including the speaker not only established solution theories for these singular SPDEs, but also led to an explosion of new questions. These include scaling limits of random microscopic models, development of numerical schemes, ergodicity of random dynamical systems and a new approach to quantum field theory. In this talk we will discuss the main ideas of the recent solution theories of singular SPDEs, and how these SPDEs arise as limits of various important physical models.
One of the central concerns of arithmetic geometry is the study of
solutions of systems of polynomial equations where the solutions are
required to lie in a "small" field such as the rational numbers. I
will explain the landscape of expectations and conjectures in this
area, focusing on curves and their Jacobians over global fields
(number fields and function fields), and then survey the progress made
over the last decade in the function field case. The talk is intended
to be accessible to a wide audience.


===Monday, December 5:  Botong Wang (UW-Madison)===
== Past Colloquia ==
Title:  Enumeration of points, lines, planes, etc.
 
Abstract: It is a theorem of de Bruijn and Erdos that n points in the plane determine at least n lines, unless all the points lie on a line. This is one of the earliest results in enumerative combinatorial geometry. We will present a higher dimensional generalization of this theorem, which confirms a “top-heavy” conjecture of Dowling and Wilson in 1975. I will give a sketch of the key ideas of the proof, which are the hard Lefschetz theorem and the decomposition theorem in algebraic geometry. I will also talk about a log-concave conjecture on the number of independent sets. These are joint works with June Huh.


=== Friday, December 9: Aaron Brown (U Chicago) ===
[[Colloquia/Blank|Blank]]
''Lattice actions and recent progress in the Zimmer program''


Abstract: The Zimmer Program is a collection of conjectures and questions regarding actions of lattices in higher-rank simple Lie groups on compact manifolds.  For instance, it is conjectured that all non-trivial volume-preserving actions are built from algebraic examples using standard constructions.  In particular—on manifolds whose dimension is below the dimension of all algebraic examples—Zimmer’s conjecture asserts that every action is finite. 
[[Colloquia/Spring2018|Spring 2018]]


I will present some background, motivation, and selected previous results in the Zimmer program.  I will then explain two of my results within the Zimmer program:
[[Colloquia/Fall2017|Fall 2017]]
(1) a solution to Zimmer’s conjecture for actions of cocompact lattices in SL(n,R) (joint with D. Fisher and S. Hurtado);
(2) a classification (up to topological semiconjugacy) of all actions on tori whose induced action on homology satisfies certain criteria (joint with F. Rodriguez Hertz and Z. Wang).


=== Monday, December 19: Andrew Zimmer (U Chicago) ===
[[Colloquia/Spring2017|Spring 2017]]
''Metric spaces of non-positive curvature and applications in several complex variables''


Abstract:  In this talk I will discuss how to use ideas from the theory of metric spaces of non-positive curvature to understand the behavior of holomorphic maps between bounded domains in complex Euclidean space. Every bounded domain has an metric, called the Kobayashi metric, which is distance non-increasing with respect to holomorphic maps. Moreover, this metric often satisfies well-known non-positive curvature type conditions (for instance, Gromov hyperbolicity or visibility) and one can then use these conditions to understand the behavior of holomorphic maps. Some of what I will talk about is joint work with Gautam Bharali.
[[Archived Fall 2016 Colloquia|Fall 2016]]
 
=== Monday, January 9: Miklos Racz (Microsoft) ===
''Statistical inference in networks and genomics''
 
Abstract: From networks to genomics, large amounts of data are increasingly available and play critical roles in helping us understand complex systems. Statistical inference is crucial in discovering the underlying structures present in these systems, whether this concerns the time evolution of a network, an underlying geometric structure, or reconstructing a DNA sequence from partial and noisy information. In this talk I will discuss several fundamental detection and estimation problems in these areas.
 
I will present an overview of recent developments in source detection and estimation in randomly growing graphs. For example, can one detect the influence of the initial seed graph? How good are root-finding algorithms? I will also discuss inference in random geometric graphs: can one detect and estimate an underlying high-dimensional geometric structure? Finally, I will discuss statistical error correction algorithms for DNA sequencing that are motivated by DNA storage, which aims to use synthetic DNA as a high-density, durable, and easy-to-manipulate storage medium of digital data.
 
=== Friday, January 13: Mihaela Ifrim (Berkeley) ===
''Two dimensional water waves''
 
The classical water-wave problem consists of solving the Euler equations in the presence of a free fluid surface (e.g the water-air interface). This talk will provide an overview of recent developments concerning the motion of a two dimensional incompressible fluid with a free surface. There is a wide range of problems that fall under the heading of water waves, depending on a number of assumptions that can be applied: surface tension, gravity, finite bottom, infinite bottom, rough bottom, etc., and combinations thereof. We will present the physical motivation for studying such problems, followed by the discussion of several interesting mathematical questions related to them. The first step in the analysis is the choice of coordinates, where multiple choices are available. Once the equations are derived we will discuss the main issues arising when analysing local well-posedness, as well as the long time behaviour of solutions with small, or small and localized data. In the last part of the talk we will introduce a new, very robust method which allows one to obtain enhanced lifespan bounds for the solutions. If time permits we will also introduce an alternative method to the scattering theory, which in some cases yields a straightforward route to proving global existence results and obtaining an asymptotic description of solutions. This is joint work with Daniel Tataru, and in part with John Hunter.
 
== Past Colloquia ==


[[Colloquia/Spring2016|Spring 2016]]
[[Colloquia/Spring2016|Spring 2016]]

Revision as of 21:57, 17 October 2018

Mathematics Colloquium

All colloquia are on Fridays at 4:00 pm in Van Vleck B239, unless otherwise indicated.

The calendar for spring 2019 can be found here.

Fall 2018

date speaker title host(s)
Sep 12 Room 911 Gunther Uhlmann (Univ. of Washington) Distinguished Lecture series Harry Potter's Cloak via Transformation Optics Li
Sep 14 Room 911 Gunther Uhlmann (Univ. of Washington) Distinguished Lecture series Journey to the Center of the Earth Li
Sep 21 Room 911 Andrew Stuart (Caltech) LAA lecture The Legacy of Rudolph Kalman Jin
Sep 28 Gautam Iyer (CMU) Stirring and Mixing Thiffeault
Oct 5 Eyal Subag (Penn State) Symmetries of the hydrogen atom and algebraic families Gurevich
Oct 12 Andrei Caldararu (Madison) Mirror symmetry and derived categories ...
Oct 19 Jeremy Teitelbaum (U Connecticut) Lessons Learned and New Perspectives: From Dean and Provost to aspiring Data Scientist Boston
Oct 26 Douglas Ulmer (Arizona) Rational numbers, rational functions, and rational points Yang
Nov 2 Reserved for job talk TBA hosting faculty
Nov 9 Reserved for job talk TBA hosting faculty
Nov 16 Reserved for job talk TBA hosting faculty
Nov 30 Reserved for job talk TBA hosting faculty
Dec 7 Reserved for job talk TBA hosting faculty

Abstracts

Sep 12: Gunther Uhlmann (Univ. of Washington)

Harry Potter's Cloak via Transformation Optics

Can we make objects invisible? This has been a subject of human fascination for millennia in Greek mythology, movies, science fiction, etc. including the legend of Perseus versus Medusa and the more recent Star Trek and Harry Potter. In the last fifteen years or so there have been several scientific proposals to achieve invisibility. We will introduce in a non-technical fashion one of them, the so-called "traansformation optics" in a non-technical fashion n the so-called that has received the most attention in the scientific literature.

Sep 14: Gunther Uhlmann (Univ. of Washington)

Journey to the Center of the Earth

We will consider the inverse problem of determining the sound speed or index of refraction of a medium by measuring the travel times of waves going through the medium. This problem arises in global seismology in an attempt to determine the inner structure of the Earth by measuring travel times of earthquakes. It has also several applications in optics and medical imaging among others.

The problem can be recast as a geometric problem: Can one determine the Riemannian metric of a Riemannian manifold with boundary by measuring the distance function between boundary points? This is the boundary rigidity problem. We will also consider the problem of determining the metric from the scattering relation, the so-called lens rigidity problem. The linearization of these problems involve the integration of a tensor along geodesics, similar to the X-ray transform.

We will also describe some recent results, join with Plamen Stefanov and Andras Vasy, on the partial data case, where you are making measurements on a subset of the boundary. No previous knowledge of Riemannian geometry will be assumed.

Sep 21: Andrew Stuart (Caltech)

The Legacy of Rudolph Kalman

In 1960 Rudolph Kalman published what is arguably the first paper to develop a systematic, principled approach to the use of data to improve the predictive capability of mathematical models. As our ability to gather data grows at an enormous rate, the importance of this work continues to grow too. The lecture will describe this paper, and developments that have stemmed from it, revolutionizing fields such space-craft control, weather prediction, oceanography and oil recovery, and with potential for use in new fields such as medical imaging and artificial intelligence. Some mathematical details will be also provided, but limited to simple concepts such as optimization, and iteration; the talk is designed to be broadly accessible to anyone with an interest in quantitative science.

Sep 28: Gautam Iyer (CMU)

Stirring and Mixing

Mixing is something one encounters often in everyday life (e.g. stirring cream into coffee). I will talk about two mathematical aspects of mixing that arise in the context of fluid dynamics:

1. How efficiently can stirring "mix"?

2. What is the interaction between diffusion and mixing.

Both these aspects are rich in open problems whose resolution involves tools from various different areas. I present a brief survey of existing results, and talk about a few open problems.

Oct 5: Eyal Subag (Penn State)

Symmetries of the hydrogen atom and algebraic families

The hydrogen atom system is one of the most thoroughly studied examples of a quantum mechanical system. It can be fully solved, and the main reason why is its (hidden) symmetry. In this talk I shall explain how the symmetries of the Schrödinger equation for the hydrogen atom, both visible and hidden, give rise to an example in the recently developed theory of algebraic families of Harish-Chandra modules. I will show how the algebraic structure of these symmetries completely determines the spectrum of the Schrödinger operator and sheds new light on the quantum nature of the system. No prior knowledge on quantum mechanics or representation theory will be assumed.

Oct 12: Andrei Caldararu (Madison)

Mirror symmetry and derived categories

Mirror symmetry is a remarkable phenomenon, first discovered in physics. It relates two seemingly disparate areas of mathematics, symplectic and algebraic geometry. Its initial formulation was rather narrow, as a technique for computing enumerative invariants (so-called Gromov-Witten invariants) of symplectic varieties by solving certain differential equations describing the variation of Hodge structure of “mirror" varieties. Over the past 25 years this narrow view has expanded considerably, largely due to insights of M. Kontsevich who introduced techniques from derived categories into the subject. Nowadays mirror symmetry encompasses wide areas of mathematics, touching on subjects like birational geometry, number theory, homological algebra, etc.

In my talk I shall survey some of the recent developments in mirror symmetry, and I will explain how my work fits in the general picture. In particular I will describe an example of derived equivalent but not birational Calabi-Yau three folds (joint work with Lev Borisov); and a recent computation of a categorical Gromov-Witten invariant of positive genus (work with my former student Junwu Tu).

Oct 19: Jeremy Teitelbaum (U Connecticut)

Lessons Learned and New Perspectives: From Dean and Provost to aspiring Data Scientist

After more than 10 years in administration, including 9 as Dean of Arts and Sciences and 1 as interim Provost at UConn, I have returned to my faculty position. I am spending a year as a visiting scientist at the Jackson Laboratory for Genomic Medicine (JAX-GM) in Farmington, Connecticut, trying to get a grip on some of the mathematical problems of interest to researchers in cancer genomics. In this talk, I will offer some personal observations about being a mathematician and a high-level administrator, talk a bit about the research environment at an independent research institute like JAX-GM, outline a few problems that I've begun to learn about, and conclude with a discussion of how these experiences have shaped my view of graduate training in mathematics.

Oct 26: Douglas Ulmer (Arizona)

One of the central concerns of arithmetic geometry is the study of solutions of systems of polynomial equations where the solutions are required to lie in a "small" field such as the rational numbers. I will explain the landscape of expectations and conjectures in this area, focusing on curves and their Jacobians over global fields (number fields and function fields), and then survey the progress made over the last decade in the function field case. The talk is intended to be accessible to a wide audience.

Past Colloquia

Blank

Spring 2018

Fall 2017

Spring 2017

Fall 2016

Spring 2016

Fall 2015

Spring 2015

Fall 2014

Spring 2014

Fall 2013

Spring 2013

Fall 2012