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= 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'''.


== Fall 2013 ==
The calendar for spring 2019 can be found [[Colloquia/Spring2019|here]].
 
==Spring 2019==


{| cellpadding="8"
{| cellpadding="8"
!align="left" | date
!align="left" | date  
!align="left" | speaker
!align="left" | speaker
!align="left" | title
!align="left" | title
!align="left" | host(s)
!align="left" | host(s)
|-
|-
|Sept 6
|Jan 25
|[http://people.math.gatech.edu/~mbaker/ Matt Baker] (Georgia Institute of Technology)
| [http://www.users.miamioh.edu/randrib/ Beata Randrianantoanina] (Miami University Ohio) WIMAW
|Riemann-Roch for Graphs and Applications
|[[#Beata Randrianantoanina (Miami University Ohio) | Some nonlinear problems in the geometry of Banach spaces and their applications ]]
|Ellenberg
| Tullia Dymarz
|-
|Sept 13
|[http://math.wisc.edu/~andrews/ Uri Andrews] (University of Wisconsin)
|A hop, skip, and a jump through the degrees of relative provability
|
|-
|Sept 20
|[http://www.math.neu.edu/people/profile/valerio-toledano-laredo Valerio Toledano Laredo] (Northeastern)
|Flat connections and quantum groups
|Gurevich
|-
|'''Wed, Sept 25, 2:30PM in B139'''
|[http://mypage.iu.edu/~alindens/ Ayelet Lindenstrauss] (Indiana University)
|Taylor Series in Homotopy Theory
|Meyer
|-
|'''Wed, Sept 25''' (LAA lecture)
|[http://www.cs.berkeley.edu/~demmel/ Jim Demmel] (Berkeley)
|Communication-Avoiding Algorithms for Linear Algebra and Beyond
|Gurevich
|-
|'''Thurs, Sept 26''' (LAA lecture, Joint with Applied Algebra Seminar)
|[http://www.cs.berkeley.edu/~demmel/ Jim Demmel] (Berkeley)
|Implementing Communication-Avoiding Algorithms
|Gurevich
|-
|Sept 27 (LAA lecture)
|[http://www.cs.berkeley.edu/~demmel/ Jim Demmel] (Berkeley)
|Communication Lower Bounds and Optimal Algorithms for Programs that Reference Arrays
|Gurevich
|-
|Oct 4
|[http://www.math.tamu.edu/~sottile/ Frank Sottile] (Texas A&M)
|Galois groups of Schubert problems
|Caldararu
|-
|Oct 11
|[http://math.uchicago.edu/~wilkinso/ Amie Wilkinson] (Chicago)
|[[Colloquia#October 11: Amie Wilkinson (Chicago)  | Robust mechanisms for chaos]]
|WIMAW (Cladek)
|-
|'''Tues, Oct 15, 4PM''' (Distinguished Lecture)
|[http://math.mit.edu/people/profile.php?pid=1222 Alexei Borodin] (MIT)
|[[Colloquia#October 15 (Tue) and October 16 (Wed): Alexei Borodin (MIT) | Integrable probability I]]
|Valko
|-
|'''Wed, Oct 16, 2:30PM''' (Distinguished Lecture)
|[http://math.mit.edu/people/profile.php?pid=1222 Alexei Borodin] (MIT)
|[[Colloquia#October 15 (Tue) and October 16 (Wed): Alexei Borodin (MIT) | Integrable probability II]]
|Valko
|-
|<strike>Oct 18</strike>
|No colloquium due to the distinguished lecture
|
|
|-
|Oct 25
|[http://www.math.umn.edu/~garrett/ Paul Garrett] (Minnesota)
|[[Colloquia#October 25: Paul Garrett (Minnesota) | Boundary-value problems, generalized functions, and zeros of zeta functions]]
|Gurevich
|
|
|-
|Nov 1
|[http://www.cs.columbia.edu/~alewko/ Allison Lewko] (Columbia University)
|On sets of large doubling, Lambda(4) sets, and error-correcting codes
|Stovall
|-
|Nov 8
|[http://www.math.cornell.edu/~riley/ Tim Riley] (Cornell)
|[[Colloquia#November 8: Tim Riley (Cornell) | Hydra groups]]
|Dymarz
|-
|Nov 15 and later
|Reserved
|
|
|Street
|-
|Nov 22
|[http://www.math.uchicago.edu/~tj/ Tianling Jin] (University of Chicago)
|Solutions of some Monge-Ampere equations with degeneracy or singularities.
|Bolotin
|-
|'''Mon, Nov 25, 4PM'''
|[https://web.math.princeton.edu/~linlin/ Lin Lin] (Lawrence Berkeley National Lab)
|Fast algorithms for electronic structure analysis
|Jin
|-
|'''Tue, Nov 26, 4PM, B139'''
|[http://www.math.cornell.edu/m/People/Faculty/conley Clinton Conley] (Cornell)
|[[Colloquia#November 26 (Tuesday): Clinton Conley (Cornell) | Descriptive set-theoretic graph theory]]
|Lempp
|-
|'''Mon, Dec 2, 4PM'''
|[http://www.math.northwestern.edu/~slm/ Simon Marshall] (Northwestern)
|[[Colloquia#December 2 (Monday): Simon Marshall (Northwestern) | Semiclassical estimates for eigenfunctions on locally symmetric spaces]]
|Denissov
|-
|'''Wed, Dec 4, 4PM'''
|[http://math.berkeley.edu/~svs/ Steven Sam] (Berkeley)
|Free Resolutions and Symmetry
|Boston
|-
|'''Fri, Dec 6'''
|[http://math.mit.edu/~hand/ Paul Hand] (MIT)
|[[Colloquia#December 6: Paul Hand (MIT)  | Simplifications of the lifting approach for quadratic signal recovery problems]]
|Thiffeault
|-
|-
|'''Fri, Dec. 6 and Sat Dec. 7'''
|Jan 30 '''Wednesday'''
|
| [https://services.math.duke.edu/~pierce/ Lillian Pierce] (Duke University)
|[http://www.math.umn.edu/~stant001/askey80 Conference in honor of Dick Askey]
|[[#Lillian Pierce (Duke University) |  Short character sums  ]]
| Boston and Street
|
|
|-
|-
|'''Mon, Dec. 9, 4pm, VV B239'''
|Jan 31 '''Thursday'''
|[http://www.cims.nyu.edu/~jacob/ Jacob Bedrossian] (Courant Institute)
| [http://www.math.tamu.edu/~dbaskin/ Dean Baskin] (Texas A&M)
|Inviscid damping and the asymptotic stability of planar shear flows in the 2D Euler equations
|[[#Dean Baskin (Texas A&M) | Radiation fields for wave equations ]]
|Bolotin
| Street
|-
|'''Wed, Dec 11, 4PM'''
|[http://math.jhu.edu/~lwang/ Lu Wang] (Johns Hopkins)
|Rigidity of Self-shrinkers of Mean Curvature Flow
|Viaclovsky
|-
|'''Fri, Dec. 13, 2:25pm, VV 901'''
|[http://chanwookim.wordpress.com/ Chanwoo Kim] (Cambridge)
|Regularity of the Boltzmann equation in convex domains
|Bolotin
|-
|'''Tues, Dec 17, 4PM'''
|[http://www.statslab.cam.ac.uk/~ps422/ Perla Sousi] (Cambridge)
|[[Colloquia#December 17: Perla Sousi (Cambridge) | The effect of drift on the volume of the Wiener sausage]]
|Seppalainen
|-
|'''Wed, Dec 18, 4PM'''
|[http://users.math.yale.edu/~dc597/ Dustin Cartwright] (Yale)
|[[Colloquia#December 18: Dustin Cartwright (Yale) | Tropical Complexes]]
|Gurevich
|}
 
== Spring 2014 ==
 
{| cellpadding="8"
!align="left" | date
!align="left" | speaker
!align="left" | title
!align="left" | host(s)
|-
|'''Mon, Jan 6, 4PM'''
|[http://www-bcf.usc.edu/~lauda/Aaron_Laudas_Page/Home.html Aaron Lauda] (USC)
|[[Colloquia#January 6: Aaron Lauda (USC) | An introduction to diagrammatic categorification]]
|Caldararu
|-
|'''Wed, Jan 8, 4PM'''
|[http://www2.math.umd.edu/~kmelnick/ Karin Melnick] (Maryland)
|[[Colloquia#January 8: Karin Melnick (Maryland) | Normal forms for local flows on parabolic geometries]]
|Kent
|-
|Jan 10, 4PM
|[http://users.math.yale.edu/~yd82/ Yen Do] (Yale)
|Convergence of Fourier series and multilinear analysis
|Denissov
|-
|'''Mon, Jan 13, 4pm'''
|[http://math.stanford.edu/~wangyi/ Yi Wang] (Stanford)
|Isoperimetric Inequality and Q-curvature
|Viaclovsky
|-
|'''Thur, Jan 16, 4pm'''
|[http://www.maths.ox.ac.uk/people/profiles/wei.xiang Wei Xiang] (University of Oxford)
|Conservation Laws and Shock Waves
|Bolotin
|-
|Jan 17
|[http://www.math.dartmouth.edu/~gillmana/ Adrianna Gillman] (Dartmouth)
|
|
|Thiffeault
|-
|'''Thu, Jan 23, 2:25, VV901'''
|[http://www.stat.berkeley.edu/~mshkolni/ Mykhaylo Shkolnikov] (Berkeley)
|[[Colloquia#Thur, Jan 23: Mykhaylo Shkolnikov (Berkeley) | Intertwinings, wave equations and growth models]]
|Seppalainen
|-
|-
|Jan 24
|Feb 1
|[http://www.yanivplan.com/ Yaniv Plan] (Stanford)
| [https://services.math.duke.edu/~jianfeng/ Jianfeng Lu] (Duke University)
|[[# TBA|  TBA  ]]
| Qin
|
|
|Thiffeault
|-
|-
|Jan 31
|Feb 5 '''Tuesday'''
|[http://csi.usc.edu/~ubli/ubli.html Urbashi Mitra] (USC)
| [http://www.math.tamu.edu/~alexei.poltoratski/ Alexei Poltoratski] (Texas A&M University)
|[[# TBA|  TBA  ]]
| Denisov
|
|
|Gurevich
|-
|-
|Feb 7
|Feb 8
|David Treumann (Boston College)
| [https://sites.math.northwestern.edu/~anaber/ Aaron Naber] (Northwestern)
|[[#Aaron Naber (Northwestern) |  A structure theory for spaces with lower Ricci curvature bounds  ]]
| Street
|
|
|Street
|-
|-
|Feb 14
|Feb 15
|[http://www.tc.columbia.edu/academics/index.htm?facid=apk16 Alexander Karp] (Columbia Teacher's College)
|  
|[[# TBA|  TBA  ]]
|
|
|
|Kiselev
|-
|-
|Feb 21
|Feb 22
|
| [https://people.math.osu.edu/cueto.5/ Angelica Cueto] (Ohio State)
|
|[[# TBA|  TBA  ]]
| Erman and Corey
|
|
|-
|-
|Feb 28
|March 4
|[http://math.nyu.edu/faculty/shelley/ Michael Shelley] (Courant)
| [http://www-users.math.umn.edu/~sverak/ Vladimir Sverak] (Minnesota) Wasow lecture
|[[# TBA| TBA ]]
| Kim
|
|
|Spagnolie
|-
|-
|March 7
|March 8
|[http://www.math.northwestern.edu/people/facultyProfiles/steve.zelditch.html Steve Zelditch] (Northwestern)
| [https://orion.math.iastate.edu/jmccullo/index.html Jason McCullough] (Iowa State)
|[[# TBA|  TBA  ]]
| Erman
|
|
|Seeger
|-
|-
|March 14
|March 15
|
| Maksym Radziwill (Caltech)
|
|[[# TBA| TBA  ]]
|
| Marshall
|-
|<strike>March 21</strike>
|'''Spring Break'''
|No Colloquium
|
|
|-
|-
|March 28
|March 29
|[http://people.math.gatech.edu/~lacey/ Michael Lacey] (GA Tech)
| Jennifer Park (OSU)
|The Two Weight Inequality for the Hilbert Transform
|[[# TBA| TBA  ]]
|Street
| Marshall
|-
|April 4
|[http://www.math.brown.edu/~res/ Richard Schwartz] (Brown)
|
|
|Mari-Beffa
|-
|-
|April 11
|April 5
|[http://www.cs.uchicago.edu/people/risi Risi Kondor] (Chicago)
| Ju-Lee Kim (MIT)
|[[# TBA|  TBA  ]]
| Gurevich
|
|
|Gurevich
|-
|-
|April 18 (Wasow Lecture)
|April 12
|[http://mathnt.mat.jhu.edu/sogge/ Christopher Sogge] (Johns Hopkins)
|  Evitar Procaccia (TAMU)
|[[# TBA|  TBA  ]]
| Gurevich
|
|
|Seeger
|-
|-
|April 25
|April 19
|[http://www.charlesdoran.net Charles Doran](University of Alberta)
| [http://www.math.rice.edu/~jkn3/ Jo Nelson] (Rice University)
|[[# TBA|  TBA  ]]
| Jean-Luc
|
|
|Song
|-
|'''Monday, April 28''' (Distinguished Lecture)
|[http://www.msri.org/people/staff/de/ David Eisenbud](Berkeley)
|A mystery concerning algebraic plane curves
|Maxim
|-
|'''Tuesday, April 29''' (Distinguished Lecture)
|[http://www.msri.org/people/staff/de/ David Eisenbud](Berkeley)
|Matrix factorizations old and new
|Maxim
|-
|'''Wednesday, April 30''' (Distinguished Lecture)
|[http://www.msri.org/people/staff/de/ David Eisenbud](Berkeley)
|Easy solution of polynomial equations over  finite fields
|Maxim
|-
|-
|May 2
|April 26
|[http://www.stat.uchicago.edu/~lekheng/ Lek-Heng Lim] (Chicago)
| [https://www.brown.edu/academics/applied-mathematics/faculty/kavita-ramanan/home Kavita Ramanan] (Brown University)
|[[# TBA|  TBA  ]]
| WIMAW
|
|
|Boston
|-
|-
|May 9
|May 3
|[http://www.ma.utexas.edu/users/rward/ Rachel Ward] (UT Austin)
| Tomasz Przebinda (Oklahoma)
|[[# TBA|  TBA  ]]
| Gurevich
|
|
|WIMAW
|}
|}


== Abstracts ==
== Abstracts ==


===Sep 6: Matt Baker (GA Tech) ===
===Beata Randrianantoanina (Miami University Ohio)===
''Riemann-Roch for Graphs and Applications''
 
We will begin by formulating the Riemann-Roch theorem for graphs due to the speaker and Norine. We will then describe some refinements and applications. Refinements include a Riemann-Roch theorem for tropical curves, proved by Gathmann-Kerber and Mikhalkin-Zharkov, and a Riemann-Roch theorem for metrized complexes of curves, proved by Amini and the speaker. Applications include a new proof of the Brill-Noether theorem in algebraic geometry (work of by Cools-Draisma-Payne-Robeva), a "volume-theoretic proof" of Kirchhoff's Matrix-Tree Theorem (work of An, Kuperberg, Shokrieh, and the speaker), and a new Chabauty-Coleman style bound for the number of rational points on an algebraic curve over the rationals (work of Katz and Zureick-Brown).
 
===Sep 13: Uri Andrews (UW-Madison) ===
''A hop, skip, and a jump through the degrees of relative provability''
 
The topic of this talk arises from two directions. On the one hand, Gödel's incompleteness theorem tell us that given any sufficiently strong, consistent, effectively axiomatizable theory T for first-order arithmetic, there is a statement that is true but not provable in T. On the other hand, over the past seventy years, a number of researchers studying witnessing functions for various combinatorial statements have realized the importance of fast-growing functions and the fact that their totality is often not provable over a given sufficiently strong, consistent, effectively axiomatizable theory T for first-order arithmetic (e.g. the Paris-Harrington and the Kirby-Paris theorems).
 
I will talk about the structure induced by giving the order (for a fixed T) of relative provability for totality of algorithms. That is, for algorithms describing functions f and g, we say f ≤ g if T along with the totality of g suffices to prove the totality of f. It turns out that this structure is rich, and encodes many facets of the nature of provability over sufficiently strong, consistent, effectively axiomatizable theories for first-order arithmetic. (Work joint with Mingzhong Cai, David Diamondstone, Steffen Lempp, and Joseph S. Miller.)
 
===Sep 20: Valerio Toledano Laredo (Northeastern)===
''Flat connections and quantum groups''
 
Quantum groups are natural deformations of the Lie algebra of
nxn matrices, and more generally of semisimple Lie algebras.
They first arose in the mid eighties in the study of solvable
models in statistical mechanics.
 
I will explain how these algebraic objects can serve as natural
receptacles for the (transcendental) monodromy of flat connections
arising from representation theory.
 
These connections exist in rational, trigonometric and elliptic
forms, and lead to quantum groups of increasing interest and
complexity.
 
===Wed, Sept 25, 2:30PM Ayelet Lindenstrauss (Indiana University)===
''Taylor Series in Homotopy Theory''
 
I will discuss Goodwillie's calculus of functors on topological spaces.  To mimic the set-up in real analysis, topological spaces are considered small if their nontrivial homotopy groups start only in higher dimensions.  They can be considered close only in relation to a map between them, but a map allows us to construct the difference between two spaces, and two spaces are close if the difference between them is small.  Spaces can be summed (in different ways) by taking twisted products of them.  It is straightforward to construct the analogs of constant, linear, and higher degree homogenous functors, and they can be assembled into "polynomials" and "infinite sums".  There are notions of differentiability and higher derivatives, of Taylor towers, and of analytic functions.
 
What might look like a game of analogies is an extremely useful tool because when one looks at functors that map topological spaces not into the category of topological spaces, but into the category of spectra (the stabilized version of the category of spaces, which will be explained), many of them are, in fact, analytic, so they can be constructed from the homogenous functors of different degrees.  And we can use appropriate analogs of calculus theorems to understand them better.  I will conclude with some recent work of Randy McCarthy and myself, applying Goodwillie's calculus to algebraic K-theory calculations.
 
===Sep 25: Jim Demmel (Berkeley) ===
''Communication Avoiding Algorithms for Linear Algebra and Beyond''
 
Algorithm have two costs: arithmetic and communication, i.e. moving data between levels of a memory hierarchy or processors over a network. Communication costs (measured in time or energy per operation) already greatly exceed arithmetic costs, and the gap is growing over time following technological trends. Thus our goal is to design algorithms that minimize communication. We present algorithms that attain provable lower bounds on communication, and show large speedups compared to their conventional counterparts. These algorithms are for direct and iterative linear algebra, for dense and sparse matrices, as well as direct n-body simulations. Several of these algorithms exhibit perfect strong scaling, in both time and energy: run time (resp. energy) for a fixed problem size drops proportionally to the number of processors p (resp. is independent of p). Finally, we describe extensions to algorithms involving arbitrary loop nests and array accesses, assuming only that array subscripts are affine functions of the loop indices.
 
===Sep 26: Jim Demmel (Berkeley) ===
''Implementing Communication Avoiding Algorithms''
 
Designing algorithms that avoiding communication, attaining
lower bounds if possible, is critical for algorithms to minimize runtime and
energy on current and future architectures. These new algorithms can have
new numerical stability properties, new ways to encode answers, and new data
structures, not just depend on loop transformations (we need those too!).
We will illustrate with a variety of examples including direct linear algebra
(eg new ways to perform pivoting, new deterministic and randomized
eigenvalue algorithms), iterative linear algebra (eg new ways to reorganize
Krylov subspace methods) and direct n-body algorithms, on architectures
ranging from multicore to distributed memory to heterogeneous.
The theory describing communication avoiding algorithms can give us a large
design space of possible implementations, so we use autotuning to find
the fastest one automatically. Finally, on parallel architectures one can
frequently not expect to get bitwise identical results from multiple runs,
because of dynamic scheduling and floating point nonassociativity;
this can be a problem for reasons from debugging to correctness.
We discuss some techniques to get reproducible results at modest cost.
 
===Sep 27: Jim Demmel (Berkeley) ===
''Communication Lower Bounds and Optimal Algorithms for Programs that Reference Arrays''
 
Our goal is to minimize communication, i.e. moving data, since it increasingly
dominates the cost of arithmetic in algorithms. Motivated by this, attainable
communication lower bounds have been established by many authors for a
variety of algorithms including matrix computations.
 
The lower bound approach used initially by Irony, Tiskin and Toledo
for O(n^3)  matrix multiplication, and later by Ballard et al
for many other linear algebra algorithms, depends on a geometric result by
Loomis and Whitney: this result bounds the volume of a 3D set
(representing multiply-adds done in the inner loop of the algorithm)
using the product of the areas of certain 2D projections of this set
(representing the matrix entries available locally, i.e., without communication).
 
Using a recent generalization of Loomis' and Whitney's result, we generalize
this lower bound approach to a much larger class of algorithms,
that may have arbitrary numbers of loops and arrays with arbitrary dimensions,
as long as the index expressions are affine combinations of loop variables.
In other words, the algorithm can do arbitrary operations on any number of
variables like A(i1,i2,i2-2*i1,3-4*i3+7*i_4,…).
Moreover, the result applies to recursive programs, irregular iteration spaces,
sparse matrices,  and other data structures as long as the computation can be
logically mapped to loops and indexed data structure accesses.
 
We also discuss when optimal algorithms exist that attain the lower bounds;
this leads to new asymptotically faster algorithms for several problems.
 
===October 4: Frank Sottile (Texas A&M) ===
''Galois groups of Schubert problems''
 
Work of Jordan from 1870 showed how Galois theory
can be applied to enumerative geometry.  Hermite earlier
showed the equivalence of Galois groups with geometric
monodromy groups, and in 1979 Harris used this to study
Galois groups of many enumerative problems.  Vakil gave
a geometric-combinatorial criterion that implies a Galois
group contains the alternating group.  With Brooks and
Martin del Campo, we used Vakil's criterion to show that
all Schubert problems involving lines have at least
alternating Galois group.  White and I have given a new
proof of this based on 2-transitivity.
 
My talk will describe this background and sketch a
current project to systematically determine Galois groups
of all Schubert problems of moderate size on all small
classical flag manifolds, investigating at least several
million problems.  This will use supercomputers employing
several overlapping methods, including combinatorial
criteria, symbolic computation, and numerical homotopy
continuation, and require the development of new
algorithms and software.
 
===October 11: Amie Wilkinson (Chicago) ===
 
''Robust mechanisms for chaos''
 
What are the underlying mechanisms for robustly chaotic behavior in smooth dynamics?
 
In addressing this question, I'll focus on the study of diffeomorphisms of a compact manifold, where "chaotic" means "mixing" and and "robustly" means "stable under smooth perturbations."  I'll describe recent advances in constructing and using tools called "blenders" to produce stably chaotic behavior with arbitrarily little effort.
 
===October 15 (Tue) and October 16 (Wed): Alexei Borodin (MIT) ===
 
''Integrable probability I and II''
 
The goal of the talks is to describe the emerging field of integrable
probability, whose goal is to identify and analyze exactly solvable
probabilistic models. The models and results are often easy to describe,
yet difficult to find, and they carry essential information about broad
universality classes of stochastic processes.
 
 
===October 25: Paul Garrett (Minnesota)===
 
''Boundary-value problems, generalized functions, and zeros of zeta functions''
 
Modern analysis (Beppo Levi, Sobolev, Friedrichs, Schwartz) illuminates work of D. Hejhal and Y. Colin de Verdiere from 30 years
ago, clarifying, as in P. Cartier's letter to A. Weil, "how the Riemann Hypothesis was not proven". (Joint with E. Bombieri.)
 
===November 1: Allison Lewko (Columbia University) ===
 
''On sets of large doubling, Lambda(4) sets, and error-correcting codes''
 
We investigate the structure of finite sets A of integers such that A+A is large, presenting a counterexample to natural conjectures in the pursuit of an "anti-Freiman" theory in additive combinatorics. We will begin with a brief history of the problem and its connection to the study of Lambda(4) sets in harmonic analysis, and then we will discuss our counterexample and its construction from error-correcting codes. We will conclude by describing some related open problems.
This is joint work with Mark Lewko.
 
===November 8: Tim Riley (Cornell)===
 
''Hydra groups''
 
A few years ago Will Dison and I constructed a family of
finitely generated groups whose workings include a string-rewriting
phenomenon of extraordinary duration which is reminiscent of Hercules'
battle with the hydra. I will describe this and the investigations it
spurred in hyperbolic geometry, combinatorial group theory, and a
problem of how to calculate efficiently with hugely compressed
representations of integers.
 
===November 22: Tianling Jin (University of Chicago)===
 
''Solutions of some Monge-Ampere equations with degeneracy or singularities''
 
We will first give a new proof of a celebrated theorem of
Jorgens which states that every classical convex solution of det(Hess
u)=1 in R^2 has to be a second order polynomial. Our arguments do not use
complex analysis, and will be applied to establish such Liouville type
theorems for solutions some degenerate Monge-Ampere equations. We will
also discuss some results on existence, regularity, classification, and
asymptotic behavior of solutions of some Monge-Ampere equations with
isolated and line singularities. This is joint work with J. Xiong.
 
===Monday, Nov 25: Lin Lin  (Lawrence Berkeley National Lab)===
 
''Fast algorithms for electronic structure analysis''
 
Kohn-Sham density functional theory (KSDFT) is the most widely used
electronic structure theory for molecules and condensed matter systems. For
a system with N electrons, the standard method for solving KSDFT requires
solving N eigenvectors for an O(N) * O(N) Kohn-Sham  Hamiltonian matrix.
The computational cost for such procedure is expensive and scales as
O(N^3).  We have developed pole expansion plus selected inversion (PEXSI)
method, in which KSDFT is solved by evaluating the selected elements of the
inverse of a series of sparse symmetric matrices, and the overall algorithm
scales at most O(N^2) for all materials including insulators,
semiconductors and metals.  The PEXSI method can be used with orthogonal or
nonorthogonal basis set, and the physical quantities including electron
density, energy, atomic force, density of states, and local density of
states are calculated accurately without using the eigenvalues and
eigenvectors.  The recently developed massively parallel PEXSI method has
been implemented in SIESTA, one of the most popular electronic structure
software using atomic orbital basis set.  The resulting method can allow
accurate treatment of electronic structure in a unprecedented scale.  We
demonstrate the application of the method for solving graphene-like
structures with more than 20,000 atoms, and the method can be efficiently
parallelized 10,000 - 100,000 processors on Department of Energy (DOE) high
performance machines.
 
===November 26 (Tuesday): Clinton Conley (Cornell)===
 
''Descriptive set-theoretic graph theory''
 
Familiar graph-theoretic problems (for example, vertex coloring) exhibit a
stark change of character when measurability constraints are placed on the
structures and functions involved. While discussing some ramifications in
descriptive set theory, we also pay special attention to interactions with
probability (concerning random colorings of Cayley graphs) and ergodic
theory (characterizing various dynamical properties of groups). The talk
will include joint work with Alexander Kechris, Andrew Marks, Benjamin
Miller, and Robin Tucker-Drob.
 
 
===December 2 (Monday): Simon Marshall (Northwestern)===
 
''Semiclassical estimates for eigenfunctions on locally symmetric spaces''
 
Let M be a compact Riemannian manifold, and f an L^2-normalised Laplace
eigenfunction on M.  If p > 2, a theorem of Sogge tells us how large the L^p
norm of f can be in terms of its Laplace eigenvalue.  For instance, when p
is infinity this is asking how large the peaks of f can be.  I will present
an analogue of Sogge's theorem for eigenfunctions of the full ring of
invariant differential operators on a locally symmetric space, and discuss
some links between this result and number theory.
 
===December 4 (Wednesday): Steven Sam (Berkeley)===
 
''Free Resolutions and Symmetry''
 
This talk is about the use of symmetry in the study of modules and free resolutions in commutative algebra and algebraic geometry, and specifically how it clarifies, organizes, and rigidifies calculations, and how it enables us to find finiteness in situations where it a priori does not seem to exist. I will begin the talk with an example coming from classical invariant theory and determinantal ideals using just some basic notions from linear algebra. Then I will explain some of my own work which builds on this setting in several directions. Finally, I'll discuss a recent program on twisted commutative algebras, developed jointly with Andrew Snowden, which formalizes the synthesis of representation theory and commutative algebra and leads to new finiteness results in seemingly infinite settings.
 
===December 6: Paul Hand (MIT)===
 
''Simplifications of the Lifting Approach for Quadratic Signal Recovery Problems''
 
Many signal recovery problems are quadratic in nature, such as phase
retrieval and sparse principal component analysis.  Such problems in
R^n can be convexified by introducing n^2 variables corresponding to
each quadratic combination of unknowns.  This approach often gives
rise to an n x n matrix recovery problem that is convex and has
provable recovery guarantees.  Because the dimensionality has been
squared, it is an important task to find simplifications that make
computation more tractable.  We will discuss two examples where the
lifting approach can be simplified while retaining recovery
guarantees.  These examples will be the phase retrieval problem and a
special case of sparse principal component analysis.
 
===December 9 (Monday): Jacob Bedrossian (Courant Institute)===
 
''Inviscid damping and the asymptotic stability of planar shear flows in the 2D Euler equations''
 
We prove asymptotic stability of shear flows close to the
planar, periodic Couette flow in the 2D incompressible Euler equations.
That is, given an initial perturbation of the Couette flow small in a
suitable regularity class, specifically Gevrey space of class smaller than
2, the velocity converges strongly in L2 to a shear flow which is also
close to the Couette flow. The vorticity is asymptotically mixed to small
scales by an almost linear evolution and in general enstrophy is lost in
the weak limit. The strong convergence of the velocity field is sometimes
referred to as inviscid damping, due to the relationship with Landau
damping in the Vlasov equations. Joint work with Nader Masmoudi.
 
===Wednesday, Dec 11: Lu Wang  (Johns Hopkins)===
 
''Rigidity of Self-shrinkers of Mean Curvature Flow''
 
The study of mean curvature flow not only is fundamental in geometry, topology and analysis, but also has important applications in applied mathematics, for instance, image processing. One of the most important problems in mean curvature flow is to understand the possible singularities of the flow and self-shrinkers, i.e., self-shrinking solutions of the flow, provide the singularity models.
 
In this talk, I will describe the rigidity of asymptotic structures of self-shrinkers. First, I show the uniqueness of properly embedded self-shrinkers asymptotic to any given regular cone. Next, I give a partial affirmative answer to a conjecture of Ilmanen under an infinite order asymptotic assumption, which asserts that the only two-dimensional properly embedded self-shrinker asymptotic to a cylinder along some end is itself the cylinder. The feature of our results is that no completeness of self-shrinkers is required.
 
The key ingredients in the proof are a novel reduction of unique continuation for elliptic operators to backwards uniqueness for parabolic operators and the Carleman type techniques. If time permits, I will discuss some applications of our approach to shrinking solitons of Ricci flow.
 
===Friday, Dec 13: Chanwoo Kim (Cambridge)===
 
''Regularity of the Boltzmann equation in convex domains''
 
A basic question about regularity of Boltzmann solutions in the presence of physical boundary conditions has been open due to characteristic nature of the boundary as well as the non-local mixing of the collision operator. Consider the Boltzmann equation in a strictly convex domain with the specular, bounce-back and diffuse boundary condition. With the aid of a distance function toward the grazing set, we construct weighted classical <math>C^{1}</math> solutions away from the grazing set for all boundary conditions. For the diffuse boundary condition, we construct <math>W^{1,p}</math> solutions for 1< p<2 and weighted <math>W^{1,p}</math> solutions for <math>2\leq p\leq \infty</math> as well. On the other hand, we show second derivatives do not exist up to the boundary in general by constructing counterexamples for all boundary conditions. This is a joint work with Guo, Tonon, Trescases.
 
===December 17: Perla Sousi (Cambridge)===
 
''The effect of drift on the volume of the Wiener sausage''


The Wiener sausage at time t is the algebraic sum of a Brownian path on [0,t] and a ball. Does the expected volume of the Wiener sausage increase when we add drift?
Title: Some nonlinear problems in the geometry of Banach spaces and their applications.
How do you compare the expected volume of the usual Wiener sausage to one defined as the algebraic sum of the Brownian path and a square (in 2D) or a cube (in higher dimensions)? We will answer these questions using their relation to the detection problem for Poisson Brownian motions, and rearrangement inequalities on the sphere (with Y. Peres). We will also discuss generalisations of this to Levy processes (with A. Drewitz and R. Sun) as well as an adversarial detection problem and its connections to Kakeya sets (with Babichenko, Peres, Peretz and Winkler).


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.


===December 18: Dustin Cartwright (Yale)===
===Lillian Pierce (Duke University)===


''Tropical Complexes''
Title: Short character sums


Tropical geometry is a way of understanding algebraic varieties by the limiting behavior of their degenerations. Through tropicalization, algebraic operations are replaced with combinatorial constructions and piecewise linear functions. I will introduce tropical complexes, which a way of understanding the geometry of algebraic varieties through combinatorics. Tropical complexes are Delta-complexes together with additional integral data, for which one has parallels and concrete comparisons with the behavior of algebraic varieties.  
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.


===January 6: Aaron Lauda (USC)===
===Dean Baskin (Texas A&M)===


''An introduction to diagrammatic categorification''
Title: Radiation fields for wave equations


Categorification seeks to reveal a hidden layer in mathematical
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.
structures. Often the resulting structures can be combinatorially
complex objects making them difficult to study. One method of
overcoming this difficulty, that has proven very successful, is to
encode the categorification into a diagrammatic calculus that makes
computations simple and intuitive.


In this talk I will review some of the original considerations that
===Aaron Naber (Northwestern)===
led to the categorification philosophy.  We will examine how the
diagrammatic perspective has helped to produce new categorifications
having  profound applications to algebra, representation theory, and
low-dimensional topology.


===January 8: Karin Melnick (Maryland)===
Title: A structure theory for spaces with lower Ricci curvature bounds.


''Normal forms for local flows on parabolic geometries''
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.


The exponential map in Riemannian geometry conjugates the differential of an isometry at a point with the action of the isometry near the point. It thus provides a linear normal form for all isometries fixing a point. Conformal transformations are not linearizable in general. I will discuss a suite of normal forms theorems in conformal geometry and, more generally, for parabolic geometries, a rich family of geometric structures of which conformal, projective, and CR structures are examples.


===January 10, 4PM: Yen Do (Yale)===
== Past Colloquia ==


''Convergence of Fourier series and multilinear analysis''
[[Colloquia/Blank|Blank]]


Almost everywhere convergence of the Fourier series of square
[[Colloquia/Fall2018|Fall 2018]]
integrable functions was first proved by Lennart Carleson in 1966, and
the proof has lead to deep developments in various multilinear settings.
In this talk I would like to introduce a brief history of the subject
and sketch some recent developments, some of these involve my joint
works with collaborators.


===Mon, January 13: Yi Wang (Stanford)===
[[Colloquia/Spring2018|Spring 2018]]


''Isoperimetric Inequality and Q-curvature''
[[Colloquia/Fall2017|Fall 2017]]


A well-known question in differential geometry is to prove the
[[Colloquia/Spring2017|Spring 2017]]
isoperimetric inequality under intrinsic curvature conditions. In
dimension 2, the isoperimetric inequality is controlled by the integral of
the positive part of the Gaussian curvature. In my recent work, I prove
that on simply connected conformally flat manifolds of higher dimensions,
the role of the Gaussian curvature can be replaced by the Branson's
Q-curvature. The isoperimetric inequality is valid if the integral of the
Q-curvature is below a sharp threshold. Moreover, the isoperimetric
constant depends only on the integrals of the Q-curvature. The proof
relies on the theory of $A_p$ weights in harmonic analysis.


===Thur, January 16: Wei Xiang (University of Oxford)===
[[Archived Fall 2016 Colloquia|Fall 2016]]


''Conservation Laws and Shock Waves''
[[Colloquia/Spring2016|Spring 2016]]


The study of continuum physics gave birth to the theory of quasilinear
[[Colloquia/Fall2015|Fall 2015]]
systems in divergence form, commonly called conservation laws. In this
talk, conservation laws, the Euler equations, and the definition of the
corresponding weak solutions will be introduced first. Then a short history
of the studying of conservation laws and shock waves will be given. Finally
I would like to present two of our current research projects. One is on the
mathematical analysis of shock diffraction by convex cornered wedges, and
the other one is on the validation of weakly nonlinear geometric optics for
entropy solutions of nonlinear hyperbolic systems of conservation laws.


===Thur, Jan 23: Mykhaylo Shkolnikov (Berkeley) ===
[[Colloquia/Spring2014|Spring 2015]]
''Intertwinings, wave equations and growth models''


We will discuss a general theory of intertwined diffusion processes of any dimension. Intertwined processes arise in many different contexts in probability theory, most notably in the study of random matrices, random polymers and path decompositions of Brownian motion. Recently, they turned out to be also closely related to hyperbolic partial differential equations, symmetric polynomials and the corresponding random growth models. The talk will be devoted to these recent developments which also shed new light on some beautiful old examples of intertwinings. Based on joint works with Vadim Gorin and Soumik Pal.
[[Colloquia/Fall2014|Fall 2014]]


===March 28: Michael Lacey (GA Tech) ===
[[Colloquia/Spring2014|Spring 2014]]
''The Two Weight Inequality for the Hilbert Transform''


The individual two weight inequality for the Hilbert transform
[[Colloquia/Fall2013|Fall 2013]]
asks for a real variable characterization of those pairs of weights
(u,v) for which the Hilbert transform H maps L^2(u) to L^2(v).
This question arises naturally in different settings, most famously
in work of Sarason. Answering in the positive a deep
conjecture of Nazarov-Treil-Volberg, the mapping property
of the Hilbert transform is characterized by a triple of conditions,
the first being a two-weight Poisson A2 on the pair of weights,
with a pair of so-called testing inequalities, uniform over all
intervals.  This is the first result of this type for a singular
integral operator.  (Joint work with Sawyer, C.-Y. Shen and Uriate-Tuero)


== Past talks ==
[[Colloquia 2012-2013|Spring 2013]]


Last year's schedule: [[Colloquia 2012-2013]]
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]

Latest revision as of 14:43, 24 January 2019

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.

Spring 2019

date speaker title host(s)
Jan 25 Beata Randrianantoanina (Miami University Ohio) WIMAW Some nonlinear problems in the geometry of Banach spaces and their applications Tullia Dymarz
Jan 30 Wednesday Lillian Pierce (Duke University) Short character sums Boston and Street
Jan 31 Thursday Dean Baskin (Texas A&M) Radiation fields for wave equations Street
Feb 1 Jianfeng Lu (Duke University) TBA Qin
Feb 5 Tuesday Alexei Poltoratski (Texas A&M University) TBA Denisov
Feb 8 Aaron Naber (Northwestern) A structure theory for spaces with lower Ricci curvature bounds Street
Feb 15 TBA
Feb 22 Angelica Cueto (Ohio State) TBA Erman and Corey
March 4 Vladimir Sverak (Minnesota) Wasow lecture TBA Kim
March 8 Jason McCullough (Iowa State) TBA Erman
March 15 Maksym Radziwill (Caltech) TBA Marshall
March 29 Jennifer Park (OSU) TBA Marshall
April 5 Ju-Lee Kim (MIT) TBA Gurevich
April 12 Evitar Procaccia (TAMU) TBA Gurevich
April 19 Jo Nelson (Rice University) TBA Jean-Luc
April 26 Kavita Ramanan (Brown University) TBA WIMAW
May 3 Tomasz Przebinda (Oklahoma) TBA Gurevich

Abstracts

Beata Randrianantoanina (Miami University Ohio)

Title: Some nonlinear problems in the geometry of Banach spaces and their applications.

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.

Lillian Pierce (Duke University)

Title: Short character sums

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.

Dean Baskin (Texas A&M)

Title: Radiation fields for wave equations

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.

Aaron Naber (Northwestern)

Title: A structure theory for spaces with lower Ricci curvature bounds.

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.


Past Colloquia

Blank

Fall 2018

Spring 2018

Fall 2017

Spring 2017

Fall 2016

Spring 2016

Fall 2015

Spring 2015

Fall 2014

Spring 2014

Fall 2013

Spring 2013

Fall 2012

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