Charles Bordenave

Title: Strong convergence of random matrices with latent geometries

Abstract:We will present recent results on the convergence of the operator norm of random matrices of large dimension. Our random matrices are build by taking tensor products of deterministic matrices and independent Haar distributed unitary matrices or independent random permutation matrices. This class of random matrices allows for example to consider random Schreier graphs of Cartesian products of free groups. They are motivated by questions in operator algebra, representation theory and spectral graph theory. The talk will be notably based on joint works with Benoit Collins.

Alison Etheridge

Title: The forwards and backwards of locally regulated populations

Abstract:We introduce a broad class of mechanistic models that might describe how spatially heterogeneous
populations live, die, and reproduce. Questions we (start to) address include: how does population density change across space and time? And how does genetic ancestry spread across geography when looking back through time in these populations? A novelty is that by explicitly splitting reproduction into two phases (production of juveniles and their maturation) we produce a framework that not only captures models that when suitably scaled converge to classical reaction diffusion equations, but also ones with nonlinear diffusion that exhibit quite different behaviour.
This is joint work with Tom Kurtz (Madison), Peter Ralph (Oregon) and Ian Letter and Terence
Tsui (Oxford).

Alessandra Faggionato

Title: Random resistor networks and low-temperature decay of conductivity

Abstract: Random resistor networks are an important tool to study electron transport in disordered media. To simultaneously treat different geometric features determined by Physics, we introduce a
general class of networks on simple point processes. Popular examples are resistor networks on Z^d or on the supercritical percolation cluster and the Miller-Abrahams resistor network. Under very basic assumptions, we derive the a.s. large scale limit of the conductivity. We then move to the low temperature regime,
where energetic barriers become extreme, thus leading to relevant and universal decay laws of conductivity such as Mott’s law for doped semiconductors. We discuss a rigorous derivation which provides the value of some constants debated in the Physics literature, clarifies universality and confirms the paradigm of Critical Path Analysis. Our investigation is based on simple point processes, stochastic homogenization and percolation theory.

Lenya Ryzhik

Title: Shape defect function and convergence to traveling waves

Abstract: It is well known that solutions to many semilinear parabolic equations
can be interpreted in terms of various functionals of branching Brownian motion, most famously so for the Fisher-KPP equation. The shape defect function is a recently reinvented convenient PDE tool that allows to analyze the convergence of the solutions to traveling waves in a very straightforward fashion. Surprisingly,
its behavior looks anomalous in the BBM context. I will explain this phenomenon and beg the audience for a probabilistic explanation.

Thursday Nov 16

9:00-9:30 Refreshments and registration
Kimmel Center, Room 912/914

9:30-10:30 Alessandra Faggionato
Kimmel Center, Room 912/914

10:30-10:45 Break

10:45-11:45 Charles Bordenave
Kimmel Center, Room 912/914

11:45-1:45 Lunch (around campus)

1:45-5:00 Short talks, coffee breaks
Kimmel Center, Room 912/914

5:30-7:00 Reception
Courant Institute, 13th Floor Lounge

Friday Nov 17

9:00-9:30 Refreshments and registration
Courant Institute, Room 109

9:30-10:30 Alison Etheridge
Courant Institute, Room 109

10:30-10:45 Break

10:45-11:45 Lenya Ryzhik
Courant Institute, Room 109

11:45-1:45 Lunch (around campus)

1:45-5:00 Short talks, coffee breaks
Courant Institute, Room 109

Thursday November 16 2023 NYU Kimmel Center, Room 914

1:45-2:45 PM
Xiao Shen
Title: Independence property of the Busemann function in exactly solvable KPZ models

Evan Sorensen
Title: Jointly invariant measures for the Kardar-Parisi-Zhang Equation

Zhengjiang Lin
Title: Topology of Gaussian Random Zero Sets

Ruixuan Zhang
Title: A conditional limit of the KPZ fixed point

Hongyi Chen
Title: Multiplicative Stochastic Heat Equation on Compact Manifolds of Nonpositive Sectional Curvature

2:45-3:00
Break

3:00-4:00
Luke Peilen
Title: Local Laws and a Mesoscopic CLT for beta-ensembles

Christine Chang
Title: Hybrid Statistics of the Maxima of a Random Model of the Zeta Function over Intervals of Varying Length

Pax Kivimae
Title: The Larkin Mass and Free Energy of The Elastic Manifold

Daesung Kim
Title: Curie-Weiss model under l^p constraint

Gursharn Kaur
Title: Interacting Urns on a Directed Network with Node-Dependent Sampling and Reinforcement

4:00-4:15
Break

4:15-4:50
Douglas Dow
Title: Differentiability of the shape function for continuous space directed polymers

Peter Rudzis
Title: Fluctuations of the Atlas model from inhomogeneous stationary profiles

Yujin Kim
Title: The shape of the front of multidimensional branching Brownian motion

Friday November 17 2023 Courant Institute, Room 109

1:45-2:45 PM
Miriam Gordin
Title: Vector-Valued Concentration on Symmetric Group

Guang Yang
Title: Coupling method and the fundamental gap problem on sphere.

Jiaming Chen
Title: New stochastic Fubini theorem via stochastic integrals of measure-valued processes

Andres Riveros
Title: Markov Process Jump Times and Their Cox Construction

Liangbing Luo
Title: Logarithmic Sobolev inequalities on homogeneous spaces

2:45-3:00
Break

3:00-4:10
Chunyin Siu
Title: Asymptotics of Expected Betti Numbers of Preferential Attachment Clique Complexes

Andrea Ottolini
Title: Hitting times on ER random graphs

Prabhanka Deka
Title: Local weak limit for the collapsed branching process with random out-degrees

Aaradhya Pandey
Title: Exact recovery in the Gaussian weighted Stochastic block model

Thanh Le Nhat Dang
Title: Density convergence of Gaussian functionals to a Gamma density via the Malliavin-Stein method

Georgy Gaitsgori
Title: A Dynkin Game with Independent Processes and Incomplete Information

4:10-4:25
Break

4:25-5:25
Matthew Nicoletti
Title: Stationary Measures of Colored Particle Systems from Yang–Baxter Equation

Mingtao Xia
Title: Kinetic theories of generation-dependent cellular proliferation models

Raghavendra Tripathi
Title: Two-color exchangeability: some observations and questions

Ella Hiesmayr
Title: The spectral edge of Erdős-Rényi graphs with constant average degree

Haixiao Wang
Title: Optimal and exact recovery for community detection on general hypergraphs