[iasmath-seminars] Mathematics Seminars -- Week of October 16, 2017

[Anthony Pulido]

INSTITUTE FOR ADVANCED STUDY
School of Mathematics
Princeton, NJ 08540

Mathematics Seminars
Week of October 16, 2017


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To view mathematics in titles and abstracts, please click on the talk's link.
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Monday, October 16

Computer Science/Discrete Mathematics Seminar I
		No seminar: FOCS
Speaker: 	No seminar: FOCS
Time/Room: 	 -

Seminar on Theoretical Machine Learning
Topic: 		Keeping IT cool: machine learning for data center cooling
Speaker: 	Nevena Lazic, Google
Time/Room: 	12:30pm - 1:45pm/White-Levy Room
Abstract Link:	http://www.math.ias.edu/seminars/abstract?event=133461

Members' Seminar
		no seminar: Hermann Weyl Lecture
Speaker: 	no seminar: Hermann Weyl Lecture
Time/Room: 	 -

Hermann Weyl Lectures
Topic: 		On the mathematical theory of black holes I
Speaker: 	Sergiu Klainerman, Princeton University
Time/Room: 	2:00pm - 3:00pm/S-101
Abstract Link:	http://www.math.ias.edu/seminars/abstract?event=128754

Princeton/IAS Symplectic Geometry Seminar
Topic: 		Compactification of moduli spaces of J-holomorphic maps relative to snc divisors
Speaker: 	Mohammad Tehrani, Stonybrook University
Time/Room: 	4:00pm - 5:00pm/Fine 224, Princeton University
Abstract Link:	http://www.math.ias.edu/seminars/abstract?event=133380



Tuesday, October 17

Locally Symmetric Spaces Seminar
Topic: 		Cohomology of arithmetic groups and automorphic forms: an introduction (continued)
Speaker: 	Laurent Clozel, Université Paris-Sud 11; Member, School of Mathematics
Time/Room: 	10:00am - 11:45am/Physics Library, Bloomberg Hall 201

Computer Science/Discrete Mathematics Seminar II
		No seminar: FOCS
Speaker: 	No seminar: FOCS
Time/Room: 	 -

Hermann Weyl Lectures
Topic: 		On the mathematical theory of black holes II
Speaker: 	Sergiu Klainerman, Princeton University
Time/Room: 	2:00pm - 3:00pm/S-101
Abstract Link:	http://www.math.ias.edu/seminars/abstract?event=132623

Locally Symmetric Spaces Seminar
Topic: 		Transfer operators for (relative) functoriality "beyond endoscopy" II
Speaker: 	Yiannis Sakellaridis, Rutgers University; von Neumann Fellow, School of Mathematics
Time/Room: 	3:15pm - 5:00pm/S-101
Abstract Link:	http://www.math.ias.edu/seminars/abstract?event=132705



Wednesday, October 18

Hermann Weyl Lectures
Topic: 		On the mathematical theory of black holes III
Speaker: 	Sergiu Klainerman, Princeton University
Time/Room: 	2:00pm - 3:00pm/S-101
Abstract Link:	http://www.math.ias.edu/seminars/abstract?event=132626

Mathematical Conversations
Topic: 		Spectral gaps without frustration
Speaker: 	Marius Lemm, California Institute of Technology; Member, School of Mathematics
Time/Room: 	6:00pm - 7:00pm/Dilworth Room
Abstract Link:	http://www.math.ias.edu/seminars/abstract?event=131210



Thursday, October 19

Working Group on Algebraic Number Theory
Speaker: 	To Be Announced
Time/Room: 	2:00pm - 4:00pm/Jadwin 111, Princeton University

Joint IAS/Princeton University Number Theory Seminar
Topic: 		The arithmetic intersection conjecture
Speaker: 	Michael Rapoport, University of Maryland/University of Bonn
Time/Room: 	4:30pm - 5:30pm/Fine 214, Princeton University
Abstract Link:	http://www.math.ias.edu/seminars/abstract?event=131085

1 Keeping IT cool: machine learning for data center cooling
    Nevena Lazic

I will describe recent efforts in using machine learning to control 
cooling in Google data centers, as well as related research in linear 
quadratic control.

http://www.math.ias.edu/seminars/abstract?event=133461

2 On the mathematical theory of black holes I
    Sergiu Klainerman

On the reality of black holes. I will give a quick introduction to the 
initial value problem in GR and overview of the problems of Rigidity, 
Stability and Collapse and how they fit with regard to the Final State 
Conjecture.

The gravitational waves detected recently by LIGO were produced in the 
final faze of the inward spiraling of two black holes before they 
collided to produce a more massive black hole. The experiment is 
entirely consistent with the so called Final State Conjecture of General 
Relativity according to which, generically, solutions of the initial 
value problem of the Einstein vacuum equations approach asymptotically, 
in any compact region, a Kerr black hole. Though the conjecture is so 
very easy to formulate and happens to be consistent with astrophysical 
observations as well as numerical experiments, its proof is far beyond 
our current mathematical understanding, let alone available techniques 
techniques. In fact even the far simpler and fundamental question of the 
stability of the Kerr black hole remains wide open.

In my lectures I will address the issue of stability as well as other 
aspects the mathematical theory of black holes such as rigidity and the 
problem of collapse. The rigidity conjecture asserts that all stationary 
solutions the Einstein vacuum equations must be Kerr black holes while 
the problem of collapse addresses the issue of how black holes form in 
the first place from regular initial conditions. Recent advances on all 
these problems were made possible by a remarkable combination of new 
geometric and analytic techniques which I will try to outline in my 
lectures.

http://www.math.ias.edu/seminars/abstract?event=128754

3 Compactification of moduli spaces of J-holomorphic maps relative to 
snc divisors
    Mohammad Tehrani

In this talk, I will describe an efficient way of compactifying moduli 
spaces of J-holomorphic maps relative to simple normal crossings (snc) 
symplectic divisors, including the holomorphic case. The primary goal of 
this construction is to define Gromov-Witten invariants relative to snc 
divisors, and to establish a GW-degeneration formula for any semistable 
degeneration with an snc central fiber. It is also possible to extend 
the construction to the case of J-holomorphic maps with boundary on a 
Lagrangian, even if the Lagrangian intersects the divisor non-trivially 
(intersecting each stratum in a Lagrangian again); especially, if the 
Lagrangian is a real locus.

http://www.math.ias.edu/seminars/abstract?event=133380

4 On the mathematical theory of black holes II
    Sergiu Klainerman

I will discuss in some detail the main difficulties of the problem of 
nonlinear stability of black holes and the recent advances on the 
related issue of linear stability.

The gravitational waves detected recently by LIGO were produced in the 
final faze of the inward spiraling of two black holes before they 
collided to produce a more massive black hole. The experiment is 
entirely consistent with the so called Final State Conjecture of General 
Relativity according to which, generically, solutions of the initial 
value problem of the Einstein vacuum equations approach asymptotically, 
in any compact region, a Kerr black hole. Though the conjecture is so 
very easy to formulate and happens to be consistent with astrophysical 
observations as well as numerical experiments, its proof is far beyond 
our current mathematical understanding, let alone available techniques 
techniques. In fact even the far simpler and fundamental question of the 
stability of the Kerr black hole remains wide open.

In my lectures I will address the issue of stability as well as other 
aspects the mathematical theory of black holes such as rigidity and the 
problem of collapse. The rigidity conjecture asserts that all stationary 
solutions the Einstein vacuum equations must be Kerr black holes while 
the problem of collapse addresses the issue of how black holes form in 
the first place from regular initial conditions. Recent advances on all 
these problems were made possible by a remarkable combination of new 
geometric and analytic techniques which I will try to outline in my 
lectures.

http://www.math.ias.edu/seminars/abstract?event=132623

5 Transfer operators for (relative) functoriality "beyond endoscopy" II
    Yiannis Sakellaridis

"Beyond endoscopy", broadly interpreted, is the idea that functoriality 
should be realized as a comparison between stable trace formulas. The 
nature of this comparison, however, remains completely unclear.

Broadening our scope to include the relative Langlands program 
(replacing groups by spherical varieties), in this series of talks we 
will revisit examples of relative trace formula comparisons that have 
appeared in the literature, and study the local "transfer operators" 
that realize these comparisons. Some structure will begin to emerge, 
that will be discussed further in subsequent talks, later in the semester.

The examples that will be discussed include:

(1) comparison between the Kuznetsov formula and the stable trace 
formula of $SL(2)$ (which first appeared in the thesis of Rudnick);

(2) comparison between the Kuznetsov formula and the relative trace 
formula for the variety $T\backslash PGL(2)$, where $T$ is a torus;

(3) comparison between the Kuznetsov formula for $GL(2)$ and the "trace 
formula" for a torus (Venkatesh's thesis).

Paradoxically (because functoriality was supposed to solve the problem 
of analytic continuation of L-functions), "beyond endoscopy" calls for 
the insertion of L-functions into trace formulas, and some treatment of 
their meromorphic continuation. This treatment is most successful when 
their functional equation can be expressed as a Poisson summation 
formula for certain "Hankel transforms" between spaces of orbital 
integrals. Thus, alongside the aforementioned transfer operators, we 
will also discuss two examples of Hankel transforms, namely:

(4) the Hankel transform for the standard L-function of $GL(n)$ on the 
Kuznetsov formula (contained in a paper of Jacquet);

(5) the Hankel transform for the symmetric square L-function of $GL(2)$ 
on the Kuznetsov formula (extracted from the Rankin–Selberg method).

Again, some structure will be visible, but we will also stumble on a 
precise local version of Sarnak's objection to the extension of these 
methods to higher symmetric powers.

http://www.math.ias.edu/seminars/abstract?event=132705

6 On the mathematical theory of black holes III
    Sergiu Klainerman

I will discuss a recent result in collaboration with J. Szeftel 
concerning the nonlinear stability of the Schwarzschild spacetime under 
axially symmetric, polarized perturbations.

The gravitational waves detected recently by LIGO were produced in the 
final faze of the inward spiraling of two black holes before they 
collided to produce a more massive black hole. The experiment is 
entirely consistent with the so called Final State Conjecture of General 
Relativity according to which, generically, solutions of the initial 
value problem of the Einstein vacuum equations approach asymptotically, 
in any compact region, a Kerr black hole. Though the conjecture is so 
very easy to formulate and happens to be consistent with astrophysical 
observations as well as numerical experiments, its proof is far beyond 
our current mathematical understanding, let alone available techniques 
techniques. In fact even the far simpler and fundamental question of the 
stability of the Kerr black hole remains wide open.

In my lectures I will address the issue of stability as well as other 
aspects the mathematical theory of black holes such as rigidity and the 
problem of collapse. The rigidity conjecture asserts that all stationary 
solutions the Einstein vacuum equations must be Kerr black holes while 
the problem of collapse addresses the issue of how black holes form in 
the first place from regular initial conditions. Recent advances on all 
these problems were made possible by a remarkable combination of new 
geometric and analytic techniques which I will try to outline in my 
lectures.

http://www.math.ias.edu/seminars/abstract?event=132626

7 Spectral gaps without frustration
    Marius Lemm

In spin systems, the existence of a spectral gap has far-reaching 
consequences. "Frustration-free" spin systems form a subclass that is 
special enough to make the spectral gap problem amenable and, at the 
same time, broad enough to be physically relevant. We discuss 
"finite-size criteria", which allow to bound the spectral gap of the 
infinite system by the spectral gap of finite subsystems. We focus on 
the connection between spectral gaps and boundary conditions.

http://www.math.ias.edu/seminars/abstract?event=131210

8 The arithmetic intersection conjecture
    Michael Rapoport

The Gan-Gross-Prasad conjecture relates the non-vanishing of a special 
value of the derivative of an L-function to the non-triviality of a 
certain functional on the Chow group of a Shimura variety. Beyond the 
one-dimensional case, there is little hope for proving this conjecture. 
I will explain a variant of this conjecture (suggested by Wei Zhang) 
which seems more accessible and report on progress on it. This is joint 
work with B. Smithling and W. Zhang.

http://www.math.ias.edu/seminars/abstract?event=131085

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http://www.math.ias.edu/seminars