News & Achievements
Welcome back! Even as we prepare for a very unusual new semester, we are very excited to be joined by a large number of newcomers this fall, and to welcome them to our Department! Regular Faculty Robert Dolan, Assistant Professor in Residence Amineh Farzannia, Assistant Professor in Residence Sijing Liu, Assistant Professor in Residence Hanson […][Read More]
Vector-Valued Modular Forms
Richard Gottesman (Queen's University)11:15am
Wednesday, September 30th, 2020
11:15 AM - 12:05 PM
Storrs Campus WebExI will give an introduction to vector-valued modular forms and describe some of my results on the arithmetic of their Fourier coefficients. The collection of vector-valued modular forms form a graded module over the graded ring of modular forms. I will explain how understanding the structure of this module allows one to show that the component functions of vector-valued modular forms satisfy an ordinary differential equation whose coefficients are modular forms. In certain cases, one may use a Hauptmodul to transform such a differential equation into a Fuchsian differential equation on the projective line minus three points. I will explain how these ideas can be used to prove certain cases of the unbounded denominator conjecture for vector-valued modular forms.
Please contact the organizer for the WebEx link.
Contact Information: firstname.lastname@example.orgMore
Differentiation Under the Integral Sign
Nicholas Juricic (UConn)5:45pm
Wednesday, September 30th, 2020
05:45 PM - 06:35 PM
Storrs Campus OnlineThe two main techniques of integration taught in calculus courses are integration by substitution and integration by parts. This talk will describe and illustrate a third technique of integration, almost never
taught in math courses, called differentiation under the integral sign. It can handle integrals that appear inaccessible to simpler methods. The physicist Richard Feynman had great affection for differentiation under the integral sign, writing once
"I caught on how to use that method, and I used that one damn tool again and again."
This talk will assume familiarity with partial derivatives from multivariable calculus.
Note: Join the meeting at https://uconnvtc.webex.com/meet/mathclub
Contact Information: Keith ConradMore
Probability And Data Science Colloquium: Ming Yuan (Columbia University))2:00pm
Thursday, October 1st, 2020
02:00 PM - 03:00 PM
Storrs Campus OnlineTitle: Information Based Complexity for High Dimensional Statistical Models
Abstract: I will introduce a coherent framework to quantify the complexity of high dimensional models that appropriately accounts for both statistical accuracy and computational cost and better understand the potential trade-off between the two types of efficiencies. As an example, I will use this notion of complexity to examine high-dimensional and sparse nonparametric problems to illustrate how this can lead to the development of novel and optimal sampling and estimation strategies, and in particular reveal the role of experimental design in alleviating computational burden.
Contact Information: Zhongyang LiMore
Math Physics Learning Seminar
Zhongshan An (University Of Connecticut)10:00am
Friday, October 2nd, 2020
10:00 AM - 11:00 AM
Storrs Campus online (please contact Masha for the link)Title: Initial boundary value problem for vacuum Einstein equations
Abstract: In general relativity, spacetime metrics are solutions to the Einstein equations, which are wave equations moduli gauge. The Cauchy problem for the vacuum Einstein equations has been well-understood since the work of Choquet-Bruhat. For certain given initial conditions, there is a geometrically unique solution to the vacuum Einstein equations. On contrast, the initial boundary value problem has been much less understood. To solve for a spacetime metric in a domain with time-like boundary, one needs to impose boundary conditions to guarantee geometric uniqueness of the solution. However, due to gauge issues occurring on the boundary, there has not been a satisfying choice of boundary conditions.
In this talk we will first talk about spacetimes, Einstein equations and the Cauchy problem. Then we will discuss obstacles to establishing a well-defined initial boundary value problem and new results on it (joint work with Michael Anderson).
Contact Information: Masha Gordina (email@example.com)More
Logic Colloquium (Online): Lenore Blume (CMU)1:00pm
Friday, October 2nd, 2020
01:00 PM - 02:30 PM
Storrs Campus onlineJoin us for a talk by Lenore Blum (Carnegie Mellon) in the Logic Colloquium!
"What Can Theoretical Computer Science Contribute to the Discussion of Consciousness?"
We propose a mathematical model, which we call the Conscious Turing Machine (CTM), as a formalization of neuroscientist Bernard Baars’ Theater of Consciousness. The CTM is proposed for the express purpose of understanding consciousness. In settling on this model, we look not for complexity but simplicity, not for a complex model of the brain or cognition but a simple mathematical model sufficient to explain consciousness. Our approach, in the spirit of mathematics and theoretical computer science, proposes formal definitions to fix informal notions and deduce consequences. We are inspired by Alan Turing’s extremely simple formal model of computation that is a fundamental first step in the mathematical understanding of computation. This mathematical formalization includes a precise definition of chunk, a precise description of the competition that Long Term Memory (LTM) processors enter to gain access to Short Term Memory (STM)), and a precise definition of conscious awareness in the model. Feedback enables LTM processors to learn from their mistakes and successes and emerging links enable conscious processing to become unconscious. The reasonableness of the formalization lies in the breadth of concepts that the model explains easily and naturally. The model provides some understanding of the Hard Problem of consciousness, which we explore in the particular case of pain and pleasure. The understanding depends on the dynamics of the CTM, not on chemicals like serotonin, dopamine, and so on. We set ourselves the problem of explaining the feeling of consciousness in ways that apply as well to machines made of silicon and gold as to animals made of flesh and blood. With regard to suggestions for AI, the CTM is well suited to giving succinct explanations for whatever high level decisions it makes. This is because the chunk in STM either articulates an explanation or points to chunks that do.
Please contact Marcus Rossberg for log-in information.
Contact Information: firstname.lastname@example.orgMore