• Speaker: Zhe Zhang (Alan)
• Title: Elliptic Regularity of J-Holomorphic Curves
• Date: 09/19/2018
• Time: 4:00 PM - 4:50 PM
• Place: A202 Wells Hall

One of the fundamental estimates for the L^p theory of elliptic operators is Calderon-Zygmund inequality. I’ll follow Mcduff & Salamon’s book for the proof of regularity theorem, raising the order of nonlinear Cauchy Riemann equation and making use of mean value property.

• Speaker: Keshav Sutrave
• Title: Take a walk on a Riemann surface
• Date: 10/03/2018
• Time: 4:10 PM - 5:00 PM
• Place: A202 Wells Hall

This talk will be an introduction to Riemann surfaces, including branched covering and monodromy in this setting. I will prove Riemann's existence theorem of branched covers, illustrate this using algebraic curves, and finish with Riemann-Hurwitz.

• Speaker: Michael Shultz
• Title: The homology polynomial and pseudo-Anosov braids
• Date: 10/17/2018
• Time: 4:10 PM - 5:00 PM
• Place: A202 Wells Hall

Every orientation preserving homeomorphism of a compact, connected, orientable surface S is isotopic to a representative that is periodic, reducible, or pseudo-Anosov (pA). In the last case, the representative is neither periodic nor reducible and the surface admits two (singular) transverse measured foliations. The pA representative "stretches" with respect to one of these measures by a number called the stretch factor. The homology polynomial, introduced by Birman, Brinkmann, and Kawamuro, is an invariant of the isotopy class and contains the stretch factor as it's largest real root. It can also distinguish some distinct pA maps with the same stretch factor. In this talk I will discuss the ideas behind the homology polynomial and how it is obtained. As time permits I will discuss some examples involving pA braids and touch on a connection with the Burau representation.

• Speaker: Wenchuan Tian
• Title: A Compactness Theorem for Rotationally Symmetric Riemannian Manifolds with Positive Scalar Curvature
• Date: 10/31/2018
• Time: 4:10 PM - 5:00 PM
• Place: A202 Wells Hall

Gromov conjectured that sequences of compact Riemannian manifolds with positive scalar curvature should have subsequences which converge in the intrinsic flat sense to limit spaces with some generalized notion of scalar curvature. In light of three dimensional examples discovered jointly with Basilio and Dodziuk, Sormani suggested that one add an hypothesis assuming a uniform lower bound on the area of a closed minimal surface. We have proven this revised conjecture in the setting where the sequence of manifolds are 3 dimensional rotationally symmetric warped product manifolds. This is a project given by professor Christina Sormani, and is joint work with Jiewon Park and Changliang Wang.

• Speaker: Hitesh Gakhar
• Title: Künneth formulae in persistent homology
• Date: 11/14/2018
• Time: 4:10 PM - 5:00 PM
• Place: A202 Wells Hall

The classical Künneth formula provides a relationship between the homology of a product space and that of its factors. In this talk, I will briefly review persistent homology and show Künneth-type theorems for it. That is, for two different notions of products, we show how the persistent homology of a filtered product space relates to that of the factor filtered spaces.

• Speaker: Brandon Bavier
• Title: TBD
• Date: 11/28/2018
• Time: 4:10 PM - 5:00 PM
• Place: A202 Wells Hall

No abstract available.