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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]].


{| cellpadding="8"
== Fall 2018 ==
!align="left" | date
!align="left" | speaker
!align="left" | title
!align="left" | host(s)
|-
|Sept 6
|[http://people.math.gatech.edu/~mbaker/ Matt Baker] (Georgia Institute of Technology)
|Riemann-Roch for Graphs and Applications
|Ellenberg
|-
|Sept 13
|[http://math.wisc.edu/~andrews/ Uri Andrews] (University of Wisconsin)
|
|
|-
|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'''
|[http://mypage.iu.edu/~alindens/ Ayelet Lindenstrauss]
|
|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)
|
|Caldararu
|-
|Oct 11
|[http://math.uchicago.edu/~wilkinso/ Amie Wilkinson] (Chicago)
|
|WIMAW (Cladek)
|-
|'''Tues, Oct 15, 4PM''' (Distinguished Lecture)
|[http://math.mit.edu/people/profile.php?pid=1222 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)
|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)
|
|Gurevich
|
|
|-
|Nov 1
|[http://www.cs.utexas.edu/~alewko/ Allison Lewko] (Microsoft Research New England)
|
|Stovall
|-
|Nov 8
|[http://www.math.cornell.edu/~riley/ Tim Riley] (Cornell)
|
|Dymarz
|-
|Nov 15 and later
|Reserved
|
|Street
|}


== Spring 2014 ==


{| 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)
|-
|-
|Jan 24
|Sep 12    '''Room 911'''
|
| [https://sites.math.washington.edu/~gunther/ Gunther Uhlmann] (Univ. of Washington) Distinguished Lecture series
|
|[[#Sep 12: Gunther Uhlmann (Univ. of Washington)|  Harry Potter's Cloak via Transformation Optics  ]]
| Li
|
|
|-
|-
|Jan 31
|Sep 14    '''Room 911'''
|[http://csi.usc.edu/~ubli/ubli.html Urbashi Mitra] (USC)
| [https://sites.math.washington.edu/~gunther/ Gunther Uhlmann] (Univ. of Washington) Distinguished Lecture series
|[[#Sep 14: Gunther Uhlmann (Univ. of Washington) |  Journey to the Center of the Earth  ]]
| Li
|
|
|Gurevich
|-
|-
|Feb 7
|Sep 21    '''Room 911'''
|David Treumann (Boston College)
| [http://stuart.caltech.edu/  Andrew Stuart] (Caltech) LAA lecture
|[[#Sep 21: Andrew Stuart (Caltech) |  The Legacy of Rudolph Kalman  ]]
| Jin
|
|
|Street
|-
|-
|Feb 14
|Sep 28
|
| [https://www.math.cmu.edu/~gautam/sj/index.html Gautam Iyer] (CMU)
|
|[[#Sep 28: Gautam Iyer (CMU)| Stirring and Mixing ]]
| Thiffeault
|
|
|-
|-
|Feb 21
|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
|
|
|-
|-
|Feb 28
|Oct 12
|
| Arie Levit (Yale)
|
|[[# TBA| TBA  ]]
|
| Gurevich
|-
|March 7
|
|
|
|
|-
|-
|March 14
|Oct 19
|
| Jeremy Teitelbaum (U Connecticut)
|
|[[# TBA| TBA  ]]
|
| Boston
|-
|<strike>March 21</strike>
|'''Spring Break'''
|No Colloquium
|
|
|-
|-
|March 28
|Oct 26
|[http://people.math.gatech.edu/~lacey/ Michael Lacey] (GA Tech)
| Douglas Ulmer (Arizona)
|The Two Weight Inequality for the Hilbert Transform
|[[# TBA| TBA  ]]
|Street
| Yang
|-
|April 4
|[https://sites.google.com/site/katejuschenko/ Kate Jushchenko] (Northwestern)
|
|
|Dymarz
|-
|-
|April 11
|Nov 2
|[http://www.cs.uchicago.edu/people/risi Risi Kondor] (Chicago)
| Reserved for job talk
|[[# TBA|  TBA  ]]
| hosting faculty
|
|
|Gurevich
|-
|-
|April 18 (Wasow Lecture)
|Nov 9
|[http://mathnt.mat.jhu.edu/sogge/ Christopher Sogge] (Johns Hopkins)
| Reserved for job talk
|[[# TBA|  TBA  ]]
| hosting faculty
|
|
|A. Seeger
|-
|-
|April 25
|Nov 16
|[http://www.charlesdoran.net Charles Doran](University of Alberta)
| Reserved for job talk
|[[# TBA|  TBA  ]]
| hosting faculty
|
|
|Song
|-
|-
|May 2
|Nov 30
|[http://www.stat.uchicago.edu/~lekheng/ Lek-Heng Lim] (Chicago)
| Reserved for job talk
|[[# TBA|  TBA  ]]
| hosting faculty
|
|
|Boston
|-
|-
|May 9
|Dec 7
|[http://www.ma.utexas.edu/users/rward/ Rachel Ward] (UT Austin)
| Reserved for job talk
|[[# TBA|  TBA  ]]
| hosting faculty
|
|
|WIMAW
|}
|}


== Abstracts ==
== Abstracts ==


===Sep 6: Matt Baker (GA Tech) ===
=== Sep 12: Gunther Uhlmann (Univ. of Washington) ===
''Riemann-Roch for Graphs and Applications''
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


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).
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:


===Sep 20: Valerio Toledano (North Eastern)===
1. How efficiently can stirring "mix"?
''Flat connections and quantum groups''


Quantum groups are natural deformations of the Lie algebra of
2. What is the interaction between diffusion and mixing.
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
Both these aspects are rich in open problems whose resolution involves tools from various different areas. I present a brief survey of existing
receptacles for the (transcendental) monodromy of flat connections
results, and talk about a few open problems.
arising from representation theory.


These connections exist in rational, trigonometric and elliptic
=== Oct 5: Eyal Subag (Penn State)===
forms, and lead to quantum groups of increasing interest and
complexity.


Symmetries of the hydrogen atom and algebraic families


===Sep 25: Jim Demmel (Berkeley) ===
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.
''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.
== Past Colloquia ==


===Sep 26: Jim Demmel (Berkeley) ===
[[Colloquia/Blank|Blank]]
''Implementing Communication Avoiding Algorithms''


Designing algorithms that avoiding communication, attaining
[[Colloquia/Spring2018|Spring 2018]]
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) ===
[[Colloquia/Fall2017|Fall 2017]]
''Communication Lower Bounds and Optimal Algorithms for Programs that Reference Arrays''


Our goal is to minimize communication, i.e. moving data, since it increasingly
[[Colloquia/Spring2017|Spring 2017]]
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
[[Archived Fall 2016 Colloquia|Fall 2016]]
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
[[Colloquia/Spring2016|Spring 2016]]
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;
[[Colloquia/Fall2015|Fall 2015]]
this leads to new asymptotically faster algorithms for several problems.


[[Colloquia/Spring2014|Spring 2015]]


[[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]]

Revision as of 10:23, 19 September 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 Arie Levit (Yale) TBA Gurevich
Oct 19 Jeremy Teitelbaum (U Connecticut) TBA Boston
Oct 26 Douglas Ulmer (Arizona) TBA 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.

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