The following is a list of seminars for the academic year of 2015-2016. Go to current schedule or 2014-2015.

If you would like to give a talk at the graduate seminar, please contact:

Seunghee Ye (syye@caltech.edu)

- Oct 6: Moduli Spaces of Curves on Grassmannians - Seunghee Ye
Speaker: Seunghee Ye

Abstract: Moduli spaces of curves are fundamental objects of study in algebraic geometry. Unfortunately, these spaces are rarely compact and there are various ways to compactify the moduli spaces. In this talk, I will present a few ways to compactify the moduli space of curves on a Grassmannian. Then, I will briefly describe a mirror symmetry result in enumerative geometry and talk about how one might hope to translate it to the case of Grassmannians.

Hide - Oct 20: Forcing - William Chan
- Nov 17: Introduction to Moduli of Elliptic Curves and Modular Forms - Majid Hadian
- Dec 1: Intro to Moduli of Elliptic Curves and Modular Forms, Part 2 - Majid Hadian
Speaker: Majid Hadian

Abstract: This is the part 2 of the introduction to elliptic curves and modular forms.

Hide - Dec 8: TBA

- April 5: Geometry, Analysis and Topology and Feynman Amplitudes - Emad Nasrollahpoursamami
Speaker: Emad Nasrollahpoursamami

Abstract: Feynman Amplitudes are certain integrals that appear in perturbative quantum field theory. It turns out that values of these integrals are “Periods” in sense of algebraic geometry. Periods are defined using a pairing between homology and algebraic de Rahm cohomology of algebraic varieties. In this talk I will define Feynman amplitudes and describe the relation to algebraic geometry.

Hide - April 12: Independence of the Axiom of Choice - William Chan
- April 19: Spectral Theory of Dynamical Systems - Peter Burton
Speaker: Peter Burton

Abstract: The Koopman operator is unitary operator canonically associated to a measure-preserving dynamical system. One of the central problems in classical ergodic theory is to understand which unitary operators can arise from measure-preserving dynamical systems. In particular, there has been extensive research on the possible spectral multiplicities of Koopman operators. We will discuss the main known results and some interesting open problems.

Hide - May 3: An Overview of Generalized Hat Problems - Connor Meehan
Speaker: Connor Meehan

Abstract: Let A be a set of agents, each of whom is wearing a hat with colour from the set K, and let V be a directed graph on A, where aVb iff agent a can see b. All agents must simultaneously guess their hat colour. I will discuss under what conditions a strategy can be formed so that only a “small” number of agents guess incorrectly. I will then use this framework to give indisputable proof that one can use set theory to predict the future.* ** Audience members must be familiar with how to wear a hat.

*Almost always **Duration for which prediction is correct not guaranteed

Hide - May 10: Algebraic Theories and Duality - Ronnie Chen
Speaker: Ronnie Chen

Abstract: We will present a general framework for duality theorems, due to Isbell, Johnstone, Tholen, and others. We will discuss how many classical duality theorems, such as Stone duality, Gelfand duality, and Pontryagin duality, fit into this framework. Along the way, we will introduce monads (in the category-theoretic sense) as an abstract notion of "algebraic theories".

Hide - May 24: Generatingfunctionology, Arithmetic and Their Geometry and Topology - Brian Hwang
Speaker: Brian Hwang

Abstract:A standard way to study an infinite sequence of numbers is to put them into a formal power series. It turns out that when such numbers are "of arithmetic origin"---e.g. are the number of ways to express a number n as a sum of k squares, or the number of partitions of n---there often exists a function whose Fourier expansion coincides with the formal power series (after a suitable reparametrization). Even more strangely, such functions are usually "highly symmetric" in that they are "almost invariant" under the action of a large group G. These hidden symmetries often point to geometric and topological properties of a G-space, and whether or not such a space exists (say, as a manifold or an algebraic variety) often reveals facts about the original arithmetic question. This has led to one of the boldest conjectures in number theory, which is that such a function ALWAYS exists for sequences "of arithmetic origin"; and stronger form, which predicts that one can construct such a function geometrically. We will mostly talk about a couple of interesting known examples and adopt an elementary approach. No prior knowledge of number theory will be assumed.

Hide - May 31: TBA
- June 7: TBA

This page was created by Seunghee Ye, 2015