[math-ias] Mathematics Seminars -- Week of September 23, 2013

[Anthony V. Pulido]

INSTITUTE FOR ADVANCED STUDY
School of Mathematics
Princeton, NJ 08540

Mathematics Seminars
Week of September 23, 2013




Monday, September 23

Computer Science/Discrete Mathematics Seminar I
Topic:         Using the DFS Algorithm for Finding Long Paths in Random and
Pseudo-Random Graphs
Speaker:     Michael Krivelevich, Tel Aviv University
Time/Room:     11:15am - 12:15pm/S-101
Abstract:    See below



Tuesday, September 24

Computer Science/Discrete Mathematics Seminar II
Topic:         Finite Field Restriction Estimates
Speaker:     Mark Lewko, Institute for Advanced Study; Member, School of
Mathematics
Time/Room:     10:30am - 12:30pm/S-101
Abstract:    See below

Short talks by postdoctoral members
Topic:         Stability and instability of black holes
Speaker:     Stefanos Aretakis, Princeton University; Member, School of
Mathematics
Time/Room:     2:00pm - 2:15pm/S-101


Topic:         Self-avoiding walks
Speaker:     Roland Bauerschmidt, University of British Columbia; Member,
School of Mathematics
Time/Room:     2:15pm - 2:30pm/S-101


Topic:         The Gan-Gross-Prasad conjecture and local relative trace
formulas
Speaker:     Raphael Beuzart-Plessis, University of British Columbia;
Member, School of Mathematics
Time/Room:     2:30pm - 2:45pm/S-101


Topic:         On universality for random matrices
Speaker:     Paul Bourgade, Harvard University; Member, School of
Mathematics
Time/Room:     4:00pm - 4:15pm/S-101


Topic:         From one Reeb orbit to two
Speaker:     Daniel Cristofaro-Gardiner, University of California,
Berkeley; Member, School of Mathematics
Time/Room:     4:15pm - 4:30pm/S-101




Wednesday, September 25

Short talks by postdoctoral members
Topic:         Edge behavior of deformed Wigner matrices
Speaker:     Kevin Schnelli, Harvard University; Member, School of
Mathematics
Time/Room:     11:00am - 11:15am/S-101


Topic:         Supersymmetric derivation of the density of states for the
Gaussian Orthogonal Ensemble
Speaker:     Mira Shamis, Princeton University; Member, School of
Mathematics
Time/Room:     11:15am - 11:30am/S-101


Topic:         Growth Rate of Eigenfunctions
Speaker:     Peng Shao, Johns Hopkins University; Member, School of
Mathematics
Time/Room:     11:30am - 11:45am/S-101


Topic:         Hamiltonian Dynamics and Morse theory
Speaker:     Doris Hein, Institute for Advanced Study; Member, School of
Mathematics
Time/Room:     2:00pm - 2:15pm/S-101


Topic:         Random band matrices as a model of quantum transport
Speaker:     Antti Knowles, Courant Institute, New York University; Member,
School of Mathematics
Time/Room:     2:15pm - 2:30pm/S-101


Non-equilibrium Dynamics and Random Matrices
Topic:         Kinetic transport in quasicrystals
Speaker:     Jens Marklof, University of Bristol
Time/Room:     4:30pm - 5:30pm/S-101
Abstract:    See below



Thursday, September 26

Princeton/IAS Symplectic Geometry Seminar
Topic:         GIT and $\mu$-GIT
Speaker:     Dietmar Salamon, ETH Zurich
Time/Room:     1:30pm - 2:30pm/West Bldg. Lect. Hall
Abstract:    See below

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 Landau-Siegel zero and spacing of zeros of L-functions
Speaker:     Yitang Zhang, University of New Hampshire
Time/Room:     4:30pm - 5:30pm/S-101
Abstract:    See below

1 Using the DFS Algorithm for Finding Long Paths in Random and
Pseudo-Random Graphs
   Michael Krivelevich

The Depth First Search (DFS) algorithm is one of the most standard graph
exploration algorithms, used normally to find the connected components of
an input graph. Though perhaps less popular than its sister algorithm,
Breadth First Search (BFS), the DFS algorithm is very simple and handy and
has many nice properties; it is particularly well suited for finding long
paths. In this talk I will discuss how basic properties of the DFS
algorithm can be exploited to argue about the (typical) existence of long
paths in random and pseudo-random graphs. Based partly on a joint work with
Benny Sudakov.

2 Finite Field Restriction Estimates
   Mark Lewko

The Kakeya and restriction conjectures are two of the central open problems
in Euclidean Fourier analysis (with the second logically implying the
first, and progress on the first typically implying progress on the
second). Both of these have formulations over finite fields. In 2008 Dvir
completely settled the finite field Kakeya conjecture, however neither his
result nor the proof method have yet yielded any progress on the finite
field restriction conjecture. In this talk I will describe some recent
progress on the finite field restriction conjecture, improving the the
exponents of Mockenhaupt and Tao. The key new ingredient is the use of
incidence / sum-product estimates. [This will be a longer version of the
talk I gave in the Princeton CCI seminar on 9/13/2013]

3 Kinetic transport in quasicrystals
   Jens Marklof

Previous studies of kinetic transport in the Lorentz gas have been limited
to cases where the scatterers are distributed at random (e.g. at the points
of a spatial Poisson process) or at the vertices of a Euclidean lattice. In
this talk I will report on recent joint work with Andreas Strombergsson
(Uppsala) on quasicrystalline scatterer configurations, which are
non-periodic, yet strongly correlated. A famous example is the vertex set
of the Penrose tiling. Our main result proves the existence of a limit
distribution for the free path length, which answers a question of
Wennberg. The limit distribution is characterised by a certain random
variable on the space of higher dimensional lattices, and is distinctly
different from the exponential distribution observed in the random setting.
I will also discuss related results for other aperiodic scatterer
configurations, such as the union of pairwise incommensurate lattices. The
key ingredients in the proofs are equidistribution theorems on homogeneous
spaces, which follow from Ratner's measure classification theorem.

4 GIT and $\mu$-GIT
   Dietmar Salamon

In this lecture I will explain the moment-weight inequality, and its role
in the proof of the Hilbert-Mumford numerical criterion for
$\mu$-stability. The setting is Hamiltonian group actions on closed Kaehler
manifolds. The major ingredients are the moment map $\mu$ and the finite
dimensional analogues of the Mabuchi functional and the Futaki invariant.
This is joint work with Valentina Georgoulas and Joel Robbin, based on
conversations with Xiuxiong Chen, Song Sun, and Sean Paul.

5 The Landau-Siegel zero and spacing of zeros of L-functions
   Yitang Zhang

Let \chi be a primitive real character. We first establish a relationship
between the existence of the Landau-Siegel zero of L(s,\chi) and the
distribution of zeros of the Dirichlet L-function L(s,\psi), with \psi
belonging to a set \Psi of primitive characters, in a region \Omega. It is
shown that if the Landau-Siegel zero exists (equivalently, L(1,\chi) is
small), then, for most \psi \in \Psi, not only all the zeros of L(s,\psi)
in \Omega are simple and lie on the critical line, but also the gaps
between consecutive zeros are close to integral multiples of the half of
the average gap. In comparison with certain conjectures on the vertical
distribution of zeros of \zeta(s), it is reasonable to believe that the gap
assertion would fail to hold. In order to derive a contradiction from the
gap assertion, we attempt to reduce the problem to evaluating a certain
discrete mean; the idea is motivated by the work of Conrey, Ghosh and Conek
on the simple zeros of \zeta(s). We shall describe the coefficient of the
main term and provide some numerical evidences. In some special cases, the
problem is further reduced to calculating small positive eigenvalues of
linear integral equations with Hermitian kernels.

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