PIMS lectures
Title: Discrete Gaussian Free Field and Invariant Measures for the Non-Linear Schr枚dinger Equation
Speaker: Kesav Krishnan, 番茄社区
Date and time:
20 Mar 2024,
9:30am -
10:30am
Location: via Zoom registration required
Read full description
For more information and registration: .
ABSTRACT:
In this talk, I will describe how certain non-linear
exponential tilts of the Discrete Gaussian Free Field yield
invariant measures for a discretized PDE, the focusing Non
Linear Schr枚dinger equation. I will briefly talk about how this
tilted measure relates to self-intersections of the random
walk on $\mathbb{Z}^{d}$. I will then describe joint work
with Partha Dey and Kay Kirkpatrick on how this measure
undergoes a phase transition in the thermodynamic limit
with general $d\geq 3$ and non-linearity $p$. I will conclude
with some new results with Gourab Ray, on the weak
convergence of the random field sampled with respect to
this measure to the massive discrete Gaussian Free Field.
SPEAKER BIO:
Kesav is a PIMS postdoctoral fellow at the University
of Victoria who works with Gourab Ray. Kesav鈥檚
academic trajectory began as an undergraduate
student in physics at the University of Delhi. After
realizing that mathematical methods (specifically
probability) excited him more, Kesav switched
track and completed his masters in mathematics
at the Indian Statistical Institute, Bangalore.
As a PhD student at the University of Illinois,
Urbana-Champaign, Kesav focused on problems
in probability that have origins in statistical and
mathematical physics. He continues to work in
this field, specifically on phase transitions in
lattice field theories and disordered models in
statistical mechanics. He is thrilled to have gotten
the opportunity to spend two years in the Pacific
Northwest and explore its spectacular natural
beauty.
Download poster (PDF).
Title: PIMS Network-Wide Colloquium Series - Complex dynamics: the real story
Speaker: Sarah Koch, University of Michigan
Date and time:
29 Feb 2024,
1:30pm -
2:30pm
Location: via Zoom Registration required
Read full description
Abstract:
We will introduce the research area of complex dynamics by studying the family of (complex) quadratic polynomials, $z->z^2+c$. Historically, mathematicians first studied the dynamics of {\em real} quadratic polynomials and then moved to the complex realm. Recently, there has been a resurgence of mathematical activity surrounding real quadratic polynomials. We will explore some well known features and some rather new features of real polynomials in contrast with those enjoyed by their complex counterparts.
Speaker Biography:
Sarah Koch is a an Arthur F. Thurnau Professor in the Department of Mathematics at the University of Michigan. Her research incorporates topology, algebraic geometry, complex analysis, and Teichmueller theory to better understand complex dynamical systems (in one and several variables) and their associated dynamical moduli spaces from both analytic and algebraic points of view.
Click here to .
Title: PIMS Network-wide Colloquium: Hamilton-Jacobi equations on the Wasserstein space on graphs
Speaker: Wilfrid Gangbo, UCLA
Date and time:
25 Jan 2024,
1:30pm -
2:30pm
Location: via Zoom registration required
Read full description
Description:
We consider metric tensors on undirected weighted graphs G, which allows us to treat P(G), the set of probability vectors on G, as a length space. On defines a divergence operator div_\mu(G) for mu in P(G), in such a way that we can use control vectors m to define paths s:[0,T] \to P(G), satisfying the system of ODEs: d\sigma/dt + div_G(m) + \hbar div_\sigma(\nabla_G log \sigma)=0. These paths serve as characteristics for Hamilton-Jacobi equations involving graph-individual noise operators. We propose a well posedness theory on P(G). (This talk is based on a joint work with C. Mou and A. Swiech)
Other Information:
Time:
All network wide colloquia take place at 1:30pm Pacific Time with a few exceptions.
Registration:
Participants and can attend any of the Colloquium talks. Please remember to download the calendar information to save the dates on your calendar. PIMS will resend the confirmation from Zoom prior to the event date.