Non-Euclidean Geometry and Modern Differential Geometry

Speaker: 

Zhiqin Lu

Institution: 

UC Irvine

Time: 

Friday, February 26, 2021 - 4:00pm to 5:00pm

Host: 

Location: 

https://uci.zoom.us/j/97641313435

In this talk, I will first give a brief history of the non-Euclidean geometry. After that, I will present the Riemann's point of view of geometry which led the modern differential geometry.

The talk will be given by zoom, the link is

https://uci.zoom.us/j/97641313435

Corona Problem in Several Complex Variables

Speaker: 

Song-Ying Li

Institution: 

UC Irvine

Time: 

Friday, February 12, 2021 - 4:00pm to 5:00pm

Host: 

Location: 

Zoom https://us02web.zoom.us/j/85954136465?pwd=RmZzNzU4TXVZOS9sSEhHRkFFa1RFUT09 Meeting ID: 859 5413 6465 Passcode: song

Corona problem was initiated from function algebra, then it became one of the most important problems in harmonic analysis and complex analysis. For the case of one complex variable, the problem was solved by L. Carleson in 1960s. In the several complex variables, the problem remains open. In this talk, I will introduce the development of the Corona Problems of one and several complex variables. I will also introduce the Hormander’s weighted L2-estimate for ∂, and demonstrate how to use the weighted L2 estimates to prove some old and new results on Corona Problem.

The Geometry of Hilbert's 13th Problem

Speaker: 

Jesse Wolfson

Institution: 

UC Irvine

Time: 

Friday, June 5, 2020 - 4:00pm to 5:00pm

Host: 

Location: 

https://zoom.us/j/8473088589

The goal of this talk is to explain how enumerative geometry can be used to simplify the solution of polynomials in one variable. Given a polynomial in one variable, what is the simplest formula for the roots in terms of the coefficients? Hilbert conjectured that for polynomials of degree 6,7 and 8, any formula must involve functions of at least 2, 3 and 4 variables respectively (such formulas were first constructed by Hamilton). In a little-known paper, Hilbert sketched how the 27 lines on a cubic surface should give a 4-variable solution of the general degree 9 polynomial. In this talk I’ll recall Klein and Hilbert's geometric reformulation of solving polynomials, explain the gaps in Hilbert's sketch and how we can fill these using modern methods. As a result, we obtain best-to-date upper bounds on the number of variables needed to solve a general degree n polynomial for all n, improving results of Segre and Brauer.

Introduction to inverse boundary problems for elliptic PDE

Speaker: 

Katya Krupchyk

Institution: 

UC Irvine

Time: 

Friday, May 29, 2020 - 4:00pm to 5:00pm

Host: 

Location: 

https://zoom.us/j/8473088589

We provide a general introduction to the field of inverse boundary problems for elliptic PDE, with the celebrated Calderon problem serving as a prototypical example. The emphasis of the talk is on the techniques based on Carleman estimates and their role in the construction of complex geometric optics solutions. We also survey some of the more recent developments, including partial data problems, inverse boundary problems on manifolds, as well as inverse boundary problems for non-linear equations.

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