[csdm-rutgers] UPDATE: Seminar added --Mathematics Seminars -- Week of September 29, 2014
Anthony Pulido
apulido at ias.edu
Mon Sep 29 11:31:54 EDT 2014
INSTITUTE FOR ADVANCED STUDY
School of Mathematics
Princeton, NJ 08540
Mathematics Seminars
Week of September 29, 2014
****UPDATE: Please note that János Kollár will now speak on Tuesday at 2pm:****
Topology of Algebraic Varieties
Topic: Szemeredi--Trotter theorems in dimension 3
Speaker: János Kollár, Princeton University; Member, School of Mathematics
Time/Room: 2:00pm - 3:00pm/S-101
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To view mathematics in titles and abstracts, please click on the talk's link.
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Monday, September 29
Computer Science/Discrete Mathematics Seminar I
Topic: Breaking \(e^n\) barrier for deterministic poly-time approximation of the permanent and settling Friedland's conjecture on the Monomer-Dimer Entropy
Speaker: Leonid Gurvits, City University of New York
Time/Room: 11:15am - 12:15pm/S-101
Abstract Link: http://www.math.ias.edu/seminars/abstract?event=52294
Members' Seminar
No seminar today
Speaker: No seminar today
Time/Room: -
Short talks by postdoctoral members
Topic: On the local geometry of the zero set of high-energy Laplace eigenfunctions
Speaker: Yaiza Canzani, Member, School of Mathematics
Time/Room: 2:00pm - 2:15pm/S-101
Topic: Persistent Sheaves for Stratified Maps
Speaker: Amit Patel, Member, School of Mathematics
Time/Room: 2:15pm - 2:30pm/S-101
Topic: Topology of toric origami manifolds
Speaker: Ana Pires, Member, School of Mathematics
Time/Room: 2:30pm - 2:45pm/S-101
Topic: Time, space and monotone circuits
Speaker: Christopher Beck, Member, School of Mathematics
Time/Room: 2:45pm - 3:00pm/S-101
Topic: Dominant irreducible representations in spectra of Cayley graphs of finite groups
Speaker: Doron Puder, Member, School of Mathematics
Time/Room: 4:00pm - 4:15pm/S-101
Topic: Are there self-similar solutions to the 3D Euler equations for incompressible fluids?
Speaker: Michael Reiterer, Member, School of Mathematics
Time/Room: 4:15pm - 4:30pm/S-101
Topic: Arthur packet through the trace formula
Speaker: Bin Xu, Member, School of Mathematics
Time/Room: 4:30pm - 4:45pm/S-101
Tuesday, September 30
Computer Science/Discrete Mathematics Seminar II
Topic: Uniform words are primitive (cont'd)
Speaker: Doron Puder, Member, School of Mathematics
Time/Room: 10:30am - 12:30pm/S-101
Abstract Link: http://www.math.ias.edu/seminars/abstract?event=63424
Topology of Algebraic Varieties
Topic: The Fano variety of lines and rationality problem for a cubic hypersurface
Speaker: Lev Borisov
Time/Room: 11:00am - 12:30pm/S-114 (Martin L. Leibowitz Room)
Abstract Link: http://www.math.ias.edu/seminars/abstract?event=64314
Topology of Algebraic Varieties
Topic: Szemeredi--Trotter theorems in dimension 3
Speaker: János Kollár, Princeton University; Member, School of Mathematics
Time/Room: 2:00pm - 3:00pm/S-101
Topology of Algebraic Varieties
Topic: Tropical currents
Speaker: June Huh, Princeton University; Veblen Fellow, School of Mathematics
Time/Room: 3:30pm - 4:30pm/S-101
Abstract Link: http://www.math.ias.edu/seminars/abstract?event=63474
Wednesday, October 1
Topology of Algebraic Varieties
Topic: The topology of proper toric maps
Speaker: Mark Andrea de Cataldo, Stony Brook University; Member, School of Mathematics
Time/Room: 11:15am - 12:15pm/S-101
Abstract Link: http://www.math.ias.edu/seminars/abstract?event=63254
Short talks by postdoctoral members
Topic: Sheaves on K3 surfaces: moduli spaces, Lagrangian fibrations, and their singularities
Speaker: Giulia Saccà, Member, School of Mathematics
Time/Room: 2:00pm - 2:15pm/S-101
Topic: Spectral and scattering features of hyperbolic manifolds
Speaker: Michael Magee, Member, School of Mathematics
Time/Room: 2:15pm - 2:30pm/S-101
Topic: Higher order curvatures and isoperimetric inequalities
Speaker: Yi Wang, Member, School of Mathematics
Time/Room: 2:30pm - 2:45pm/S-101
Topic: Dynamics and birational geometry
Speaker: John Lesieutre, Member, School of Mathematics
Time/Room: 4:00pm - 4:15pm/S-101
Topic: Cylindrical contact homology in dimension 3 via intersection theory and more
Speaker: Joanna Nelson, Member, School of Mathematics
Time/Room: 4:15pm - 4:30pm/S-101
Topic: Finding rational curves by forgetful map
Speaker: Runpu Zong, Member, School of Mathematics
Time/Room: 4:30pm - 4:45pm/S-101
Thursday, October 2
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: The standard \(L\)-function for \(G_2\): a "new way"
Speaker: Nadia Gurevich, Ben-Gurion University of the Negev
Time/Room: 4:30pm - 5:30pm/S-101
Abstract Link: http://www.math.ias.edu/seminars/abstract?event=60795
1 Breaking \(e^n\) barrier for deterministic poly-time approximation of
the permanent and settling Friedland's conjecture on the Monomer-Dimer
Entropy
Leonid Gurvits
Two important breakthroughs on the permanent had been accomplished in
1998: A. Schrijver proved Schrijver-Valiant Conjecture on the minimal
exponential growth of the number of perfect matchings in k-regular
bipartite graphs with multiple edges; N. Linial, A. Samorodnitsky and A.
Wigderson introduced a strongly poly-time deterministic algorithm to
approximate the permanent of general non-negative matrices within the
multiplicative factor en. Many things happened since them, notably the
prize-winning Jerrum, Vigoda, Sinclair FPRAS for the permanent.
Schrijver's lower bound was vastly generalized and improved; moreover
the new proofs, based on hyperbolic(aka stable) polynomials, are
transparent, easy, non-computational. Yet, until now there were no
deterministic poly- time algorithms to approximate the permanent of
general non-negative matrices within the multiplicative factor \(F^n\),
\(F < e\). We prove the following double-sided inequality for
doubly-stochastic matrices \(A\): \[ \prod_{1 \leq i,j \leq n} (1 -
A(i,j))^{1-A(i,j)} \leq per(A) \leq C^n \prod_{1 \leq i,j \leq n} (1 -
A(i,j))^{1-A(i,j)},\] where \(C \approx 1.9022\). Thus a simple(of
linear complexity) extension of the scaling algorithm approximates the
permanent within the multiplicative factor \( \approx 1.9022^n\). A
slightly more involved argument proves S. Friedland's conjecture on the
Monomer-Dimer Entropy, which is a generalization of Schrijver-Valiant
Conjecture to partial matchings(aka dimers) that in the limit cover a
given fraction \(t \in [0, 1]\) of vertices. The main result in this
direction is asymptotically sharp lower bounds on the coefficients of
the weighted matching polynomial associated with a doubly-stochastic
matrix. We note that such polynomials played crucial role in the recent
breakthrough on the existence of “large” bipartite regular Ramunajan
Graphs with prescribed degree. The talk is for general
mathematical/computer science/physics audience. I will gently go through
the very rich and surprising history of the topic: amazingly, the
popular statistical physics(and lately machine learning) heuristic,
called Bethe Approximation, is one of the (completely rigorous) keys in
our approach. The Bethe Approximation was already applied by physicists
to the Monomer-Dimer Problem in late 1930s and was mysteriously hidden
in Schrijver’s 1998 paper. Time permitting, a conjecture, connecting the
Bethe Approximation, Correlation Inequalities and hyperbolic
polynomials, will be stated and discussed. (Joint work with Alex
Samorodnitsky (Hebrew University).)
http://www.math.ias.edu/seminars/abstract?event=52294
2 Uniform words are primitive (cont'd)
Doron Puder
Let \(G\) be a finite group, and let \(a\), \(b\), \(c\),... be
independent random elements of \(G\), chosen at uniform distribution.
What is the distribution of the element obtained by a fixed word in the
letters \(a\), \(b\), \(c\),..., such as \(ab\), \(a^2\), or
\(aba^{-2}b^{-1}\)? More concretely, do these new random elements have
uniform distribution? In general, a word \(w\) in the free group \(F_k\)
is called uniform if it induces the uniform distribution on every finite
group \(G\). So which words are uniform? A large set of uniform words
are those which are 'primitive' in the free group \(F_k\), namely those
belonging to some basis (a free generating set) of \(F_k\). Several
mathematicians have conjectured that primitive words are the only
uniform words. In a joint work with O. Parzanchevski, we prove this
conjecture. I will try to define and explain all notions, and give many
details from the proof. I will also present related open problems.
http://www.math.ias.edu/seminars/abstract?event=63424
3 The Fano variety of lines and rationality problem for a cubic
hypersurface
Lev Borisov
The relevant preprints are: arXiv:1405.5154 "The Fano variety of lines
and rationality problem for a cubic hypersurface", Sergey Galkin, Evgeny
Shinder arXiv:1405.4902 "On two rationality conjectures for cubic
fourfolds", Nicolas Addington
http://www.math.ias.edu/seminars/abstract?event=64314
4 Tropical currents
June Huh
I will outline a construction of "tropical current", a positive closed
current associated to a tropical variety. I will state basic properties
of tropical currents, and discuss how tropical currents are related to a
version of Hodge conjecture for positive currents. This is an ongoing
joint work with Farhad Babaee.
http://www.math.ias.edu/seminars/abstract?event=63474
5 The topology of proper toric maps
Mark Andrea de Cataldo
I will discuss some of the topology of the fibers of proper toric maps
and a combinatorial invariant that comes out of this picture. Joint with
Luca Migliorini and Mircea Mustata.
http://www.math.ias.edu/seminars/abstract?event=63254
6 The standard \(L\)-function for \(G_2\): a "new way"
Nadia Gurevich
We consider a Rankin-Selberg integral representation of a cuspidal (not
necessarily generic) representation of the exceptional group \(G_2\).
Although the integral unfolds with a non-unique model, it turns out to
be Eulerian and represents the standard \(L\)-function of degree 7. We
discuss a general approach to the integrals with non-unique models. The
integral can be used to describe the representations of \(G_2\) for
which the (twisted) \(L\)-function has a pole as functorial lifts. This
is a joint work with Avner Segal.
http://www.math.ias.edu/seminars/abstract?event=60795
IAS Math Seminars Home Page:
http://www.math.ias.edu/seminars
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