Graduate Student Seminars

Graduate Student Seminar

Mohammed Ghoneim
University of Miami

Lagrangian Floer Homology and Fukaya Category

Friday, October 3, 2025, 4:30pm
Ungar 411

Abstract: Floer homology plays a key role in the topology of 3- and 4-dimensional manifolds. In this talk, we'll introduce Lagrangian Floer homology and how it relates to instanton Floer homology through the Atiyah-Floer conjecture. We then discuss Fukaya categories as a more general construction that is richer in structure and provides more information about the Lagrangians in a symplectic manifold.

Faculty/Graduate Student Seminar

Bruno Benedetti
University of Miami

Simplicial Complexes and Decompositions of Manifolds

Friday, September 26, 2025, 4:30pm
Ungar 506

Abstract: Every manifold can be decomposed M into balls of the same dimension, with prescribed intersections. This is called a "handle decomposition of M". We sketch one (and if time permits, two) ways to interpret this notion combinatorially, that is, in the language of "simplicial complexes".

One is a bridge towards face numbers of simplicial complexes; the other one, completely unrelated, is a bridge towards a simple way to explain homotopy.

This is partly joint work with Karim Adiprasito.

Graduate Student Seminar

Andres David Ramirez Ruiz
University of Miami

Introduction to Seiberg-Witten Invariants

Friday, September 19, 2025, 4:30m
Ungar 411

Abstract: I will introduce the Seiberg-Witten equations and the associated monopole moduli space. Then I will comment on how the Seiberg-Witten invariants are constructed and give some sample theorems that can be proven with them.

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