Faculty/Graduate Student Seminar
Bruno De Oliveira
University of Miami
On the Absence of Symmetric Differentials on Horikawa Surfaces
Friday, October 24, 2025, 4:30pm
Ungar 506
Abstract: At the end of the lecture, we describe recent work on the absence of symmetric differentials on Horikawa surfaces. The lecture will start by introducing the main concepts and the circles ideas to lead to the title of the talk, e.g. classification schemes (Kodaira dimension, cotangent dimension, and the geography of surfaces of general type) and hyperbolicity of complex manifolds. We also describe previous work that led to the conjecture that surfaces of general type with Chern ratio c^2_1/c_2<1/5 have no symmetric differentials or (weaker) have non-big cotangent bundles.
Faculty/Graduate Student Seminar
Mina Teicher
University of Miami
How Does the Brain Work?
Friday, October 10, 2025, 4:30pm
Ungar 506
Abstract: In this talk, I will review the current challenges in neuroscience, the existing brain imaging devices, and the projects I am currently working on. In particular:
First, I will describe the model of brain activity that I believe in. Second, I will explain our machine learning algorithm for localizing the epileptic focus. Third, I will outline an algorithm we developed for the mind-reading of numbers.
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.
