College of Liberal Arts and Sciences

# Department of Mathematics

## Analysis Learning Seminar

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Title: Hodge theory on manifolds with boundary I
Speaker: Lihan Wang (University of Connecticut)
Time: Friday, February 2, 2018 at 3:30 pm
Place: MONT 314Abstract: In differential geometry, Hodge theory is well known and fundamental. In this sequence of talks, we will focus on the case of manifolds with boundary. We start with Riemannian case , then go to Symplctic case. We will try to use simple language to make it accessible for everyone.

Title: Hodge theory on manifolds with boundary II
Speaker: Lihan Wang (University of Connecticut)
Time: Friday, February 9, 2018 at 3:30 pm
Place: MONT 314Abstract: In differential geometry, Hodge theory is well known and fundamental. In this sequence of talks, we will focus on the case of manifolds with boundary. We start with Riemannian case , then go to Symplctic case. We will try to use simple language to make it accessible for everyone.

Title: Hodge theory on manifolds with boundary III
Speaker: Lihan Wang (University of Connecticut)
Time: Friday, February 16, 2018 at 3:30 pm
Place: MONT 314Abstract: In differential geometry, Hodge theory is well known and fundamental. In this sequence of talks, we will focus on the case of manifolds with boundary. We start with Riemannian case , then go to Symplctic case. We will try to use simple language to make it accessible for everyone.

Title: Harmonic Measure
Speaker: Matthew Badger (University of Connecticut)
Time: Friday, February 23, 2018 at 1:30 pm
Place: MONT 313Abstract: I will give a gentle introduction to harmonic measure, a fascinating object associated to any Euclidean domain which arises in complex analysis, partial differential equations, and probability theory. The first half of the talk will focus on definitions and basic examples. The second half of the talk will give a flavor of contemporary research questions about harmonic measure. No previous exposure to this topic is required.

Title: Applications of Multiplicative LLN and CLT to Random Matrices
Speaker: Raji Majumdar and Anthony Sisti (University of Connecticut)
Time: Friday, March 2, 2018 at 3:30 pm
Place: MONT 314Abstract: The Lyapunov exponent is the exponential growth rate of the operator norm of the partial products of a sequence of independent and identically distributed random matrices. It usually cannot be computed explicitly from the distribution of the matrices. Furstenberg and Kesten (1960) and Le Page (1982) found analogues to the Law of Large Numbers and Central Limit Theorem, respectively, for the norm of the partial products of a sequence of such random matrices. We use these analogues to efficiently compute the Lyapunov exponent for several random matrix models and numerically estimate the corresponding variances. For random matrices of order 2, with independent components distributed as $\xi\textrm{Bernoulli}(\frac{1}{2})$, where $\xi\in\mathbb{R}$, we obtain analytic estimates for the Lyapunov exponent in terms of a limit involving Fibonacci-like sequences.

Title: TBA
Speaker: Lisa Naples (University of Connecticut)
Time: Friday, March 23, 2018 at 3:30 pm
Place: MONT 314

Title: TBA
Speaker: Zhongyang Li (University of Connecticut)
Time: Friday, March 30, 2018 at 3:30 pm
Place: MONT 314

Title: TBA
Speaker: Christopher Hayes (University of Connecticut)
Time: Friday, April 6, 2018 at 3:30 pm
Place: MONT 314

Title: TBA
Speaker: Sean Li (University of Connecticut)
Time: Friday, April 27, 2018 at 3:30 pm
Place: MONT 314