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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
|Jan 30 '''Wednesday'''
|[http://www.math.umn.edu/~garrett/ Paul Garrett] (Minnesota)
| [https://services.math.duke.edu/~pierce/ Lillian Pierce] (Duke University)
|
|[[#Lillian Pierce (Duke University) | Short character sums  ]]
|Gurevich
| Boston and Street
|
|
|
|-
|-
|Nov 1
|Jan 31 '''Thursday'''
|[http://www.cs.columbia.edu/~alewko/ Allison Lewko] (Columbia University)
| [http://www.math.tamu.edu/~dbaskin/ Dean Baskin] (Texas A&M)
|[[#Dean Baskin (Texas A&M) | Radiation fields for wave equations  ]]
| Street
|
|
|Stovall
|-
|Nov 8
|[http://www.math.cornell.edu/~riley/ Tim Riley] (Cornell)
|
|Dymarz
|-
|Nov 15 and later
|Reserved
|
|Street
|}
== Spring 2014 ==
{| cellpadding="8"
!align="left" | date
!align="left" | speaker
!align="left" | title
!align="left" | host(s)
|-
|-
|Jan 24
|Feb 1
|[http://homepages.math.uic.edu/~mpopa/ Mihnea Popa] (UIC)
| [https://services.math.duke.edu/~jianfeng/ Jianfeng Lu] (Duke University)
|[[# TBA|  TBA  ]]
| Qin
|
|
|Arinkin
|-
|-
|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
|[http://math.nyu.edu/faculty/shelley/ Michael Shelley] (Courant)
| [https://people.math.osu.edu/cueto.5/ Angelica Cueto] (Ohio State)
|[[# TBA|  TBA  ]]
| Erman and Corey
|
|
|Spagnolie
|-
|-
|Feb 28
|March 4
|
| [http://www-users.math.umn.edu/~sverak/ Vladimir Sverak] (Minnesota) Wasow lecture
|
|[[# TBA| TBA ]]
| Kim
|
|
|-
|-
|March 7
|March 8
|
| [https://orion.math.iastate.edu/jmccullo/index.html Jason McCullough] (Iowa State)
|
|[[# TBA|  TBA  ]]
| Erman
|
|
|-
|-
|March 14
|March 15
|Temporarily reserved
| Maksym Radziwill (Caltech)
|
|[[# TBA| TBA  ]]
|Spagnolie
| 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
|
|
|A. 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
Title: Some nonlinear problems in the geometry of Banach spaces and their applications.
forms, and lead to quantum groups of increasing interest and
complexity.


===Wed, Sept 25, 2:30PM Ayelet Lindenstrauss (Indiana University)===
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.
''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.
===Lillian Pierce (Duke University)===


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.
Title: Short character sums


===Sep 25: Jim Demmel (Berkeley) ===
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.
''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.
===Dean Baskin (Texas A&M)===


===Sep 26: Jim Demmel (Berkeley) ===
Title: Radiation fields for wave equations
''Implementing Communication Avoiding Algorithms''


Designing algorithms that avoiding communication, attaining
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.
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) ===
===Aaron Naber (Northwestern)===
''Communication Lower Bounds and Optimal Algorithms for Programs that Reference Arrays''


Our goal is to minimize communication, i.e. moving data, since it increasingly
Title:  A structure theory for spaces with lower Ricci curvature bounds.
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
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.
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;
== Past Colloquia ==
this leads to new asymptotically faster algorithms for several problems.


===October 4: Frank Sottile (Texas A&M) ===
[[Colloquia/Blank|Blank]]
''Galois groups of Schubert problems''


Work of Jordan from 1870 showed how Galois theory
[[Colloquia/Fall2018|Fall 2018]]
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
[[Colloquia/Spring2018|Spring 2018]]
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) ===
[[Colloquia/Fall2017|Fall 2017]]


''Robust mechanisms for chaos''
[[Colloquia/Spring2017|Spring 2017]]


What are the underlying mechanisms for robustly chaotic behavior in smooth dynamics?
[[Archived Fall 2016 Colloquia|Fall 2016]]


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.
[[Colloquia/Spring2016|Spring 2016]]


===October 15 (Tue) and October 16 (Wed): Alexei Borodin (MIT) ===
[[Colloquia/Fall2015|Fall 2015]]


''Integrable probability I and II''
[[Colloquia/Spring2014|Spring 2015]]


The goal of the talks is to describe the emerging field of integrable
[[Colloquia/Fall2014|Fall 2014]]
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.


===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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