Colloquia & Seminars

Representations and Geometry Seminar

Title: "Applications of Algebraic Geometry in Chemical Reaction Network Theory"

Jose E. Lozano
Graduate Student, University of Texas at Arlington

When: Friday, October 6th starting at 3:30pm

Where: Pickard Hall, Room 311

Abstract: Chemical Reaction Network Theory (CRNT) is an area of mathematics that attempts to model the dynamical behavior of (bio)chemical systems. These models are represented by systems of ordinary differential equations (ODEs), often involving many unknown parameters. The aim of this presentation is to demonstrate how techniques from real and computational algebraic geometry are used to analyze such systems of ODEs. This presentation is based on material learned by the speaker at the SL Math (formerly MSRI) workshop Algebraic Methods for Biochemical Reaction Networks, which took place at the Max Planck Institute of Mathematics in Leipzig, Germany, in June 2023.

Title: "(Group) Symmetry: A Designing Principle of Neural Information Processing in the Brain?"

Wenhao Zhang, Ph.D.
Assistant Professor, UT Southwestern Medical Center

When: Friday, September 1, 2023, 2-3pm

Where: Pickard Hall, Room 311

Abstract: Equivariant representation is necessary for the brain and artificial perceptual systems to faithfully represent the stimulus under some (Lie) group transformations. However, it remains unknown how recurrent neural circuits in the brain represent the stimulus equivariantly, nor the neural representation of abstract group operators. In this talk, I will present my recent attempts to narrow down this gap. We recently used the one-dimensional translation group and the temporal scaling group as examples to explore the general recurrent neural circuit mechanism of the equivariant stimulus representation. We found that a continuous attractor network (CAN), a canonical neural circuit model, self-consistently generates a continuous family of stationary population responses (attractors) that represents the stimulus equivariantly. We rigorously derived the representation of group operators in the circuit dynamics. The derived circuits are comparable with concrete neural circuits discovered in the brain and can reproduce neuronal responses that are consistent with experimental data. Our model for the first time analytically demonstrates how recurrent neural circuitry in the brain achieves equivariant stimulus representation.
Short Bio: Dr. Wenhao Zhang is an assistant professor at UT Southwestern Medical Center studying theoretical neuroscience. A distinguished feature of his studies is that it tightly combines normative theories and biologically plausible neural circuit models to study the principles of neural information processing in the brain. His research has been published in both high-profile neuroscience journals as well as leading machine learning conferences. Before joining UT Southwestern, he did his postdoc at the University of Chicago, the University of Pittsburgh, and Carnegie Mellon University.