This seminar is meant for anyone who wishes to learn about the universe and its laws through a clear mathematical lens. Our speakers include undergraduate and graduate students, postdoctoral researchers, and professors from around the world, connected by their dedication to the mathematical analysis of problems in fundamental physics. Our talks are intended for a wide audience, including expert professors, graduate students, undergraduate students, and anyone inbetween. Its organizers are also dedicated to providing a platform for mathematicians and physicists from underpresented groups to present their research to a wide audience.

Date: 09/07/2023

Speaker: Filip Dul

Abstract: Although integration is something we usually associate with analysis (for good reason), an “algebraic essence” can be extracted from it that allows us to analyze it in a different context. In our case, this context is homological algebra. In this first lecture of a two-part series, we will explain how perturbative quantum field theory can be recast somewhat rigorously as a deformation of a homological algebraic object.

Date: 09/21/2023

Speaker: Shadi Tahvildar-Zadeh

Abstract: In this joint work with Rutgers undergraduates Suchindram Dasgupta and Chirag Khurana, we study the spectrum of the Dirac Hamiltonian in one space dimension for a single electron in the electrostatic potential of a point nucleus, in the Born-Oppenheimer approximation where the nucleus is assumed fixed at the origin. The potential is screened at large distances so that it goes to zero exponentially at spatial infinity. We show that the Hamiltonian is essentially self-adjoint, the essential spectrum has the usual gap (-m,m) in it, and that there are only finitely many eigenvalues in that gap, corresponding to ground and excited states for the system. We find a one-to-one correspondence between the eigenfunctions of this Hamiltonian and the winding number of heteroclinic saddle-saddle connectors for a certain dynamical system on a finite cylinder. We use this correspondence to study how the number of bound states changes with the nuclear charge.

Date: 10/05/2023

Speaker: Michael Kiessling (Rutgers NB)

Abstract: It is presumably safe to assume that most people have heard of the phenomenon of superconductivity, fewer know precisely what the phenomenon is. Physics students surely learn what the phenomenon is, and also learn that the BCS theory (named after Bardeen, Cooper, and Schriefer, who won a Nobel prize for their theory) explains how quantum physics causes this phenomenon. But even most physics students may never hear about the Eliashberg theory of superconductivity (true for me, when I studied physics). In this talk to mathematical physics-minded students I assume that the audience knows not even the basic condensed matter theory. So I'll be starting from there and go all the way to the latest mathematical insights into Eliashberg theory. Of course, I explain why I am doing what I am doing and why you might want to care.

If you have any questions or inquiries, please email Shadi Tahvildar-Zadeh at: shadit@math.rutgers.edu

or Lawrence Frolov at: laf230@math.rutgers.eduTo recieve notifications regarding our seminar, join our mailing list by contacting online_math_phys_sem-owner@email.rutgers.edu