Math Seminar: Limit theorems for branching diffusion processes
Dr. Pratima Hebbar, Assistant Professor, Department of Mathematics, Duke University
November 12th, 2021
10:00 AM
BSB 132
Abstract: We describe the behavior of branching diffusion processes in periodic media. For a super-critical branching process, we distinguish two types of behavior for the normalized number of particles in a bounded domain, depending on the distance of the domain from the region where the bulk of the particles is located. At distances that grow linearly in time, we observe intermittency (i.e., the k−th moment dominates the k−th power of the first moment for some k), while, at distances that grow sub-linearly in time, we show that all the moments converge.
Math Seminar: The twistor space of even Clifford Structures
Dr. Gerardo Arizmendi Echegaray, Departamento de Actuaría (Department of Actuary), La Universidad de las Américas Puebla (UDLAP)
October 29th, 2021
11:00 AM
BSB 132
Abstract: Clifford structures are generalizations of Hermitian(Kahler) and Quaternionic (QK) manifolds. In this talk, we describe even Clifford structures and describe the geometry of the Twistor Space of Even Clifford structures, making a comparison with the Twistor space of QK manifolds.
Math Seminar: Deligne’s Inequality and a Lower Bound for Ramanujan’s Tau Function
Dr. Will Lee, Professor of Mathematics, Rutgers University
October 15th, 2021
11:00 AM
BSB 132
Abstract: Here we give a stronger version of Lehmer’s Conjecture that | τ (p)| > (1/ 𝑝3, which implies the Lehmer’s Conjecture. We then establish the sharp lower bound, | τ (p)| > 𝑝4, using basically the same method as the first one. Remarkably, A(p) turned to be periodic or semi periodic from which we get the sharp lower bound.
Math Seminar: On Lehmer’s Conjecture
Dr. Will Lee, Professor of Mathematics, Rutgers University
October 8th, 2021
11:00 AM
BSB 132
Abstract: In this talk, we give a proof of the long standing Lehmer conjecture that the Ramanujan tau function τ (n) is not equal to zero. We use the Unique Factorization Theorem and the matrix attached to prime divisor q (>q) of A(p) where τ(p)=A(p)-B(p).
Math Seminar: Applications of Calculus in Lie Algebra
Dr. Haisheng Li, Professor of Mathematics, Rutgers University
October 1st, 2021
11:00 AM
BSB 132
Abstract: In this talk, we show how some simple facts in Calculus can be applied to study modules for Heisenberg Lie algebras. This is an introductory talk on Lie algebras. No knowledge beyond basic linear algebra is required. We shall begin with the definitions of Lie algebra, Heisenberg Lie algebra, and module for a Lie algebra.