I am hosting the analysis seminar for the 2025 spring semester.
Talks will be given in Little Hall 423 on Fridays during period 6 (12:50-1:40 pm).
Here is the list of speaker:
| Speaker | Date | Topic | Topic Description | |
|---|---|---|---|---|
| Arya Memana | 14 February | Free Probability and the Central Limit Theorem | In this talk, we will introduce fundamental concepts in Free Probability Theory. We will also present a combinatorial proof sketch of the classical and free central limit theorems. | |
| David Maynoldi | 21 February | Testing Von-Neumann's Inequality on Matrices | This talk is based on a new paper which gives an alternative proof of a known method for testing Von-Neumann's Inequality. The main result says that instead of testing the inequality on all tuples of commuting contractive operators on a Hilbert space, we can just test on tuples of commuting contractive nilpotent matrices. We will discuss how Caratheodory interpolation and cone separation is used to prove this result. We will state analogous results for testing on tuples of simultaneously diagonalizable contractive matrices. | |
| Lodewyk Jansen van Rensburg | 28 February | On the Connection Between Multipliers of the Drury-Averson Space and Non-commutative Hardy Space via Realizations. | The Drury-Arveson space and Non-Commutative Hardy space arise naturally in operator theory, function theory, and nc-function theory. In this talk, we explore the connections between their multiplier algebras, focusing on the transition between the commutative and non-commutative setting. A key tool in this passage is the use of realizations, which allows us to characterize their closed unit balls. We will discuss how these techniques allow us to bridge the two settings and mention successful application to characterizing extreme points. | |
| Dr. Michael Hartz | 7 March | Von Neumann's inequality on the polydisc | The classical von Neumann inequality shows that for any contraction T on a Hilbert space, the operator norm of p(T) satisfies 
Whereas Ando extended this inequality to pairs of commuting contractions, the corresponding statement for triples of commuting contractions is false. However, it is still not known whether von Neumann's inequality for triples of commuting contractions holds up to a constant. I will talk about this question and about the function theoretic upper bounds for ||p(T)||. | |
| Dr. Woongbae Park | 14 March | Introduction to Regularized n-Conformal Heat Flow |  | |
| Vangmay Jayant | 28 March | |||
| Pranav Chinmay | 4 April | |||
| Jacob Levenson | 9 April | |||
| Dr. Eric Evert | 11 April | |||
| Dr. Michael Jury | 18 April | |||