[math-ias] Mathematics Seminars -- Week of December 5, 2016

[Anthony Pulido]

INSTITUTE FOR ADVANCED STUDY
School of Mathematics
Princeton, NJ 08540

Mathematics Seminars
Week of December 5, 2016


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To view mathematics in titles and abstracts, please click on the talk's 
link.
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Monday, December 5

Computer Science/Discrete Mathematics Seminar I
Topic: 		On the number of ordinary lines determined by sets in complex space
Speaker: 	Shubhangi Saraf, Rutgers University
Time/Room: 	11:15am - 12:15pm/S-101
Abstract Link:	http://www.math.ias.edu/seminars/abstract?event=104234

Members' Seminar
Topic: 		Types and their applications
Speaker: 	Ju-Lee Kim, Massachusetts Institute of Technology; Member, 
School of Mathematics
Time/Room: 	1:15pm - 2:15pm/S-101
Abstract Link:	http://www.math.ias.edu/seminars/abstract?event=47592



Tuesday, December 6

Homological Mirror Symmetry Reading Group
Topic: 		Gamma-integral structures reading group
Speaker: 	To Be Announced
Time/Room: 	10:30am - 12:00pm/Dilworth Room

Computer Science/Discrete Mathematics Seminar II
Topic: 		Approximate constraint satisfaction requires sub-exponential 
size linear programs
Speaker: 	Pravesh Kothari, Member, School of Mathematics
Time/Room: 	10:30am - 12:30pm/S-101
Abstract Link:	http://www.math.ias.edu/seminars/abstract?event=104474

Princeton/IAS Symplectic Geometry Seminar
Topic: 		Contact manifolds with flexible fillings
Speaker: 	Oleg Lazarev, Stanford University
Time/Room: 	3:00pm - 4:00pm/Fine 224, Princeton University
Abstract Link:	http://www.math.ias.edu/seminars/abstract?event=113205

Auroux Watching Seminar
Topic: 		To Be Announced
Speaker: 	To Be Announced
Time/Room: 	5:00pm - 7:00pm/S-101



Wednesday, December 7

Working Seminar on Representation Theory
Topic: 		Mirror symmetry on the Bruhat-Tits building and representations 
of $p$-adic groups
Speaker: 	Dmitry Vaintrob, Member, School of Mathematics
Time/Room: 	11:00am - 12:00pm/S-101
Abstract Link:	http://www.math.ias.edu/seminars/abstract?event=117645

Reading Group on Homological Mirror Symmetry and K3 Surfaces
Topic: 		To Be Announced
Speaker: 	To Be Announced
Time/Room: 	1:00pm - 2:30pm/Dilworth Room

Analysis Math-Physics Seminar
Topic: 		Introduction to many-body localization
Speaker: 	David Huse, Princeton University; Member, School of Natural 
Sciences
Time/Room: 	2:00pm - 3:00pm/S-101

Mathematical Conversations
Topic: 		Negative correlation and Hodge-Riemann relations
Speaker: 	June Huh, Princeton University; Veblen Fellow, School of 
Mathematics
Time/Room: 	6:00pm - 7:00pm/Dilworth Room
Abstract Link:	http://www.math.ias.edu/seminars/abstract?event=103464



Thursday, December 8

Working Group on Algebraic Number Theory
Speaker: 	To Be Announced
Time/Room: 	2:00pm - 4:00pm/S-101

Joint IAS/Princeton University Number Theory Seminar
Topic: 		Arithmetic and geometry of Picard modular surfaces
Speaker: 	Dinakar Ramakrishnan, California Institute of Technology; 
Visitor, School of Mathematics
Time/Room: 	4:30pm - 5:30pm/S-101
Abstract Link:	http://www.math.ias.edu/seminars/abstract?event=114965

1 On the number of ordinary lines determined by sets in complex space
    Shubhangi Saraf

Consider a set of $n$ points in $\mathbb R^d$. The classical theorem of 
Sylvester-Gallai says that, if the points are not all collinear then 
there must be a line through exactly two of the points. Let us call such 
a line an "ordinary line". In a recent result, Green and Tao were able 
to give optimal linear lower bounds (roughly $n/2$) on the number of 
ordinary lines determined $n$ non-collinear points in $\mathbb R^d$. In 
this talk we will consider the analog over the complex numbers. While 
the Sylvester-Gallai theorem as stated above is known to be false over 
the field of complex numbers, it was shown by Kelly that for a set of 
$n$ points in $\mathbb C^d$, if the points don’t all lie on a 
$2$-dimensional plane then the points must determine an ordinary line. 
Using techniques developed for bounding the rank of design matrices, we 
will show that such a point set must determine at least $3n/2$ ordinary 
lines, except in the trivial case of $n - 1$ of the points being 
contained in a $2$ dimensional plane.

http://www.math.ias.edu/seminars/abstract?event=104234

2 Types and their applications
    Ju-Lee Kim

Representations of open compact subgroups play a fundamental role in 
studying representations of $p$-adic groups and their covering groups. 
We give an overview of this subject, called the theory of types, in 
connection with harmonic analysis. We will also discuss some explicit 
construction and their applications.

http://www.math.ias.edu/seminars/abstract?event=47592

3 Approximate constraint satisfaction requires sub-exponential size 
linear programs
    Pravesh Kothari

We show that for constraint satisfaction problems (CSPs), 
sub-exponential size linear programming relaxations are as powerful as 
$n^{\Omega(1)}$-rounds of the Sherali-Adams linear programming 
hierarchy. As a corollary, we obtain sub-exponential size lower bounds 
for linear programming relaxations that beat random guessing for many 
CSPs such as MAX-CUT and MAX-3SAT. This is a nearly-exponential 
improvement over previous results; previously, it was only known that 
linear programs of size $\sim n^{(\log n)}$ cannot beat random guessing 
for any CSP [Chan-Lee-Raghavendra-Steurer 2013]. Our bounds are obtained 
by exploiting and extending the recent progress in communication 
complexity for "lifting" query lower bounds to communication problems. 
The main ingredient in our results is a new structural result on 
"high-entropy rectangles" that may of independent interest in 
communication complexity. Based on joint work with Raghu Meka and Prasad 
Raghavendra.

http://www.math.ias.edu/seminars/abstract?event=104474

4 Contact manifolds with flexible fillings
    Oleg Lazarev

In this talk, I will prove that all flexible Weinstein fillings of a 
given contact manifold have isomorphic integral cohomology. As an 
application, I will show that in dimension at least 5 any almost contact 
class that has an almost Weinstein filling has infinitely many different 
contact structures. Using similar methods, I will construct the first 
known infinite family of almost symplectomorphic Weinstein domains whose 
contact boundaries are not contactomorphic. These results are proven by 
studying Reeb chords of loose Legendrians and using positive symplectic 
homology.

http://www.math.ias.edu/seminars/abstract?event=113205

5 Mirror symmetry on the Bruhat-Tits building and representations of 
$p$-adic groups
    Dmitry Vaintrob

It is an old question in representation theory whether any 
finitely-generated smooth representation of a $p$-adic group has a 
resolution by representations induced from (finite-dimensional 
representations of) compact subgroups. We construct such a resolution in 
a non-unique way, with non-uniqueness coming from a choice of lifting of 
the representation to the "compactified category" of Bezrukavnikov and 
Kazhdan. The machinery for constructing the resolution starting from an 
object of the compactified category involves techniques coming from 
mirror symmetry.

http://www.math.ias.edu/seminars/abstract?event=117645

6 Negative correlation and Hodge-Riemann relations
    June Huh

All finite graphs satisfy the two properties mentioned in the title. I 
will explain what I mean by this, and speculate on generalizations and 
interconnections.

http://www.math.ias.edu/seminars/abstract?event=103464

7 Arithmetic and geometry of Picard modular surfaces
    Dinakar Ramakrishnan

Of interest are (i) the conjecture of Bombieri (and Lang) that for any 
smooth projective surface $X$ of general type over a number field $k$, 
the set $X(k)$, of $k$-rational points is not Zariski dense, and (ii) 
the conjecture of Lang that $X(k)$, is even finite if in addition $X$ is 
hyperbolic, i.e., there is no non-constant holomorphic map from the 
complex line $C$ into $X(C)$. We can verify them for the Picard modular 
surfaces $X$ which are smooth toroidal compactifications of congruence 
quotients $Y$ of the unit ball in $\mathbb C^2$. We will describe an 
ongoing program, with Mladen Dimitrov, to prove moreover that for 
suitable deep levels, $Y$ has no rational points over the natural field 
of definition $k$. We use the theory of automorphic forms on the 
associated unitary group in three variables, and some geometry, to adapt 
and develop an analogue of the elegant method of Mazur proving such a 
result for modular curves (in 1977). We use the residual and cuspidal 
quotients of the Albanese variety of $X$, and a suitable product of such 
provides a replacement for Mazur's Eisenstein quotient. If time permits, 
we will also explain the connection to the problem of uniform 
boundedness of torsion for principally polarized abelian threefolds $A$ 
with multiplication by the ring of integers of an imaginary quadratic field.

http://www.math.ias.edu/seminars/abstract?event=114965

IAS Math Seminars Home Page:
http://www.math.ias.edu/seminars