[math-ias] IAS Math Seminars -- Week of November 12, 2012
Dottie Phares
phares at ias.edu
Thu Nov 8 13:21:12 EST 2012
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PLEASE NOTE: Change of location for Mathematical Conversations
on Wednesday, November 14, 2012
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INSTITUTE FOR ADVANCED STUDY
School of Mathematics
Princeton, NJ 08540
Mathematics Seminars
Week of November 12, 2012
Monday, November 12
Computer Science/Discrete Mathematics Seminar I
Speaker: No Seminar (Oberwolfach)
Time/Room: 11:15am - 12:15pm/S-101
Members Seminar
Topic: Proof of a 35 Year Old Conjecture for the Ent4ropy
of SU(2) Coherent States, and its Generalization.
Speaker: Elliot Lieb, Princeton University
Time/Room: 2:00pm - 3:00pm/S-101
Abstract: See below
Univalent Foundations Tutorial
Time/Room: 4:00pm - 5:30pm/S-101
Tuesday, November 13
Computer Science/Discrete Mathematics Seminar II
Speaker: No Seminar (Oberwolfach)
Time/Room: 10:30am - 12:30pm/S-101
Working Group on Univalent Foundations
Time/Room: 1:30pm - 2:45pm/S-101
Analysis Seminar
Topic: A Non-Commutative Analog of the 2-Wasserstein
Metric for which the Fermionic Fokker-Planck Equation is Gradient Flow for
the Entropy
Speaker: Eric Carlen, Rutgers, The State University of New
Jersey
Time/Room: 3:15pm - 4:15pm/S-101
Abstract: See below
Wednesday, November 14
Univalent Foundations Seminar
Topic: Toward Higher Inductive Types
Speaker: Michael Shulman, University of California, San Diego;
Member, School of Mathematics
Time/Room: 11:00am - 12:30pm/S-101
Working Group on Univalent Foundations
Time/Room: 1:30pm - 3:00pm/S-101
Mathematical Conversations
Topic: The Prisoner's Dilemma
Speaker: Freeman J. Dyson, Professor Emeritus, School of
Natural Sciences, IAS
Time/Room: 6:00pm - 7:30pm/S-101
Abstract: See below
Thursday, November 15
Univalent Foundations Seminar
Topic: The Simplicial Model of UA
(continued)
Speaker: Chris Kapulkin, Visiting Student, School of
Mathematics
Time/Room: 11:00am - 12:30pm/S-101
Working Group on Algebraic Number Theory
Time/Room: 2:00pm - 4:00pm/S-101
Joint IAS/PU Number Theory Seminar
Topic: Galois Representations for Regular Algebraic
Cuspidal Automorphic Forms
Speaker: Richard Taylor, Professor, School of Mathematics, IAS
Time/Room: 4:30pm - 5:30pm/S-101
Abstract: See below
Friday, November 16
Working Group on Univalent Foundations
Time/Room: 11:00am - 12:30pm/S-101
Joint IAS-PU Symplectic Geometry Seminar
Topic: Abstract Analogues of Flux as Symplectic
Invariants
Speaker: Paul Seidel, Massachusetts Institute of Technology
Time/Room: 4:30pm - 5:30pm/S-101
Abstract: See below
1 Proof of a 35 Year Old Conjecture for the Ent4ropy of SU(2)
Coherent States, and its Generalization.
Elliot Lieb
35 years ago Wehrl defined a classical entropy of a quantum density matrix
using Gaussian
(Schr\"odinger, Bargmann, ...) coherent states. This entropy, unlike other
classical
approximations, has the virtue of being positive. He conjectured that the
minimum entropy occurs for
a density matrix that is itself a projector onto a coherent state and this
was proved about a year
later. It was then conjectured that the same thing would occur for SU(2)
coherent states (maximal
weight vectors in a representation of SU(2)). This conjecture, and a
generalization of it, have now
been proved with J.P. Solovej. (arxiv: 1208.3632).
After a review of coherent states in general, a summary of the proof will be
given. Obviously, one
would like to prove similar conjectures for SU(n) and other Lie groups.
This is open and the
audience is invited to join the fun. Another question the audience is
invited to think about is the
meaning of all this for group representation theory. If this conjecture is
correct, it must have
some general significance
2 A Non-Commutative Analog of the 2-Wasserstein Metric for which
the Fermionic Fokker-Planck Equation is Gradient Flow for the Entropy
Eric Carlen
The Fermionic Fokker-Planck equation is a quantum-mechanical analog of the
classical Fokker-Planck
equation with which it has much in common, such as the same optimal
hypercontractivity properties.
In this paper we construct a Riemannian metric on the space of density
matrices that we show to be a
natural analog of the classical $2$-Wasserstein metric, and we show that, in
analogy with the
classical case, the Fermionic Fokker-Planck equation is gradient flow in
this metric for the
relative entropy with respect to the ground state. We derive a number of
consequences of this, such
as a sharp Talagrand inequality for this metric, and we prove a number of
results pertaining to this
metric. Several open problems are raised. This is joint work with Jann
Maas.
3 The Prisoner's Dilemma
Freeman J. Dyson
The game of Prisoner's Dilemma is the simplest non-trivial game for two
players. It has been studied
by game-theory experts for fifty years. So it came as a big surprise this
year when Bill Press
discovered a new set of strategies which allow one player to dominate the
other. The game is taken
seriously by evolutionary biologists as a model for the evolution of
cooperation in a society of
selfish individuals. Press's new strategies give us new ways of being nasty,
making the evolution of
cooperation more difficult. I will end with reasons for being skeptical of
the relevance of this
model to the evolution of cooperation in the real world.
4 Galois Representations for Regular Algebraic Cuspidal
Automorphic Forms
Richard Taylor
To any essentially self-dual, regular algebraic (ie cohomological)
automorphic representation of
GL(n) over a CM field one knows how to associate a compatible system of
l-adic representations.
These l-adic representations occur (perhaps slightly twisted) in the
cohomology of a Shimura
variety. Recently Harris, Lan, Thorne and myself have constructed l-adic
representations without the
essentially self-dual `hypothesis'. In this case the l-adic representations
do not occur in the
cohomology of any Shimura variety. Rather we construct them using a
congruence argument. In this
talk I will describe this theorem and sketch the proof.
5 Abstract Analogues of Flux as Symplectic Invariants
Paul Seidel
This talk is part of a circle of ideas that one could call ``categorical
dynamics''. We look at how
objects of the Fukaya category move under deformations prescribed by fixing
an odd degree quantum
cohomology class. This is an analogue of moving Lagrangian submanifolds
under non-Hamiltonian
deformations. It leads to a new invariant of closed symplectic manifolds,
which can distinguish
deformation equivalent symplectic structures.
IAS Math Seminars Home Page:
http://www.math.ias.edu/seminars
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