Hunter Math & Stat Colloquium

January 29 

(First week of classes)

February 5 (Recording)

Lianghao Cao, Caltech (Department of Computational and Mathematical Sciences)

Title:  Operator Learning for Predictive Scientific Computing

   Abstract: Simulation-based predictions are increasingly driving high-stakes decisions that affect our welfare and security, yet building trust in these predictions remains a fundamental challenge. In this talk, I show how operator learning can be tailored to enable reliable, predictive scientific computing that would otherwise be intractable. I focus on the design of architectures and learning formulations for two problems central to this goal: inelastic homogenization in multiscale modeling and amortized Bayesian inversion in uncertainty quantification. I conclude by outlining opportunities for future research.

February 12

(College Closed)

February 19 (Meet the Faculty)

Vincent Martinez, Hunter College (Department of Mathematics and Statistics)

Title: Finite-dimensionality in fluids and applications

   Abstract: Fluids can be described by partial differential equations (PDEs). As such, their solutions are typically given by functions of several variables. In the modern theory of PDEs, solutions are viewed as belonging to vector spaces whose elements are functions; these spaces are typically infinite-dimensional. For instance, if one insists on solutions having “finite energy,” then it is often natural to assume that solutions should be elements of the vector space of square-integrable functions. This talk will present the fundamental equations of incompressible fluids in a simplified setting that allows one to see its infinite-dimensional nature, but nevertheless demonstrate that their long-time behavior is, in some sense, finite-dimensional. We will then discuss the importance of this property in the context of turbulence and weather prediction.

February 26 (Recording)

Jinghao Cao, Caltech (Department of Computational and Mathematical Sciences)

Title: Mathematical and Computational Methods for Wave Propagation

   Abstract: This presentation first establishes a mathematical foundation for metamaterial design from a functional analytical perspective. I examine, both analytically and numerically, how symmetry breaking generates exotic wave phenomena. The framework is further extended through the development of fast, high-accuracy algorithms for PDEs in complex domains, bridging mathematical analysis and computation. 

March 5 (Meet the Faculty)

Olympia Hadjiliadis, Hunter College (Department of Mathematics and Statistics)

Title: Speed-based Measures of Signal-to-Noise Ratios

   Abstract: We present an innovative method to measure the signal-to-noise ratio in a Brownian motion model. That is, the ratio of the mean to the standard deviation of the Brownian motion. Our method is based on a method of moments estimation of the drawdown and drawup speeds in a Brownian motion model, where the drawdown process is defined as the current drop of the process from the running maximum and the drawup process is the current rise of the process above the running minimum respectively. The speed of a drawdown of K units (or a drawup of K units) is then the time between the last maximum (or minimum) of the process and the time the drawdown (or drawup) process hits the threshold K. We compare this estimator to the UMVUE and discuss its advantages. 

March 12

Abhijit Campanerkar, College of Staten Island (Department of Mathematics) and Graduate Center, CUNY

Title: Graphs, growth and geometry

   Abstract: We study the growth rate of the number of spanning trees of a sequence of planar graphs that diagrammatically converge to a planar lattice graph.  A surprising fact about the spanning tree entropy for many planar lattice graphs is that its value is closely related to hyperbolic geometry. We conjecture sharp upper and lower bounds for the spanning tree entropy of any planar lattice graph. We explain the context and recent progress for our conjecture, which lies at the intersection of hyperbolic geometry, knot theory, number theory, probability, and graph theory.

March 19 (Meet the Faculty)

Matthew Durham, Hunter College (Department of Mathematics and Statistics)

Title: To be announced

   Abstract: To be announced

March 26

Speaker, Institution (Department)

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April 2

(Spring Break)

April 9 

(Spring Break)

April 16

Ian Dryden, University of South Carolina (Department of Statistics)

Title: To be announced

   Abstract: To be announced

April 23

Parker Evans, Washington University St. Louis (Department of Mathematics)

Title: 

    Abstract: 

April 30

Lisa Carbone, Rutgers University (Department of Mathematics)

Title: To be announced

   Abstract: To be announced

May 7

Harald Helfgott, CNRS/Institut Mathématique de Jussieu (Director of Research)

Title: To be announced

   Abstract: To be announced

May 14 (Student Research Presentations)

Speakers, Institution (Department)

Title: 

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