The conference will by located at 1925 N 12th Street, Philadelphia, PA 19122, in SERC (the Science Education and Research Center).
About
This conference aims to expose graduate students in algebra, geometry, and topology to current research, and provide them with an opportunity to present and discuss their own research.
It also intends to provide a forum for graduate students to engage with each other as well as expert faculty members in their areas of research.
Most of the talks at the conference will be given by graduate students, with four given by distinguished keynote speakers.
The organizers of the GTA Philly Conference share the values and commitment to promoting diversity, equity, and inclusion as expressed by the American Mathematical Society.
"The American Mathematical Society recognizes the breadth of people, thought, and experience that contribute to mathematics.
We value the contributions of all members of our mathematics community to improve mathematics research, education, and the standing of the mathematical sciences.
We welcome everyone interested in mathematics as we work to build a community that is diverse, respectful, accessible, and inclusive.
We are committed to ensuring equitable access to mathematics opportunities and resources for people regardless of gender, gender identity or expression, race, color, national or ethnic origin, religion or religious belief, age, marital status, sexual orientation, disabilities, veteran status, immigration status, or any other social or physical component of their identity."
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Registration
The deadline to register for funding is April 11th, after which it will be considered on a rolling basis. There is no registration fee. Members of gender, racial, and ethnic groups underrepresented in mathematics are encouraged to register.
To register, please fill out this Google Form: GTA Philly 2022 Registration
Title/Abstract Submission
The deadline to submit a title/abstract for a talk is April 11th, after which they will be considered on a rolling basis.
To submit a title/abstract, please fill out this Google Form: GTA Philly 2022 Title/Abstract Submission
Abstract: We show that for almost every translation surface the number of pairs of saddle connections with bounded virtual area has asymptotic growth like $cR^2$ where the constant $c$ depends only on the area and the connected component of the stratum. The proof techniques combine classical results for counting saddle connections with the crucial result that the Siegel-Veech transform is in $L^2$. In order to capture information about pairs of saddle connections, we consider pairs with bounded virtual area since the set of such pairs can be approximated by a fibered set which is equivariant under geodesic flow. In the case of lattice surfaces, small virtual area is equivalent to counting parallel pairs of saddle connections, which also have a quadratic growth of $cR^2$ where $c$ depends in this case on the given lattice surface. This is joint work with Samantha Fairchild and Howard Masur.
Title: Enumerative Geometry, Quantum Cohomology, and Beyond
Abstract: Enumerative geometry is the art of counting geometric objects satisfying various conditions. Indeed, when Hilbert listed 23 important unsolved problems for the twentieth century, his Fifteenth Problem was to understand the methods developed by nineteenth century algebraic geometers. I will describe some underlying structures that encode the numbers. For example, a breakthrough in the 1990’s inspired by physics gave surprising and beautiful answers to classical enumerative geometry problems such as the enumeration of degree d rational plane curves passing through 3d-1 general points. I will also discuss some recent developments, including applications as well as work on equivariant and K-theoretic extensions of these structures.
Title: Floer Theoretic Invariants of Three-Manifolds and their Localization
Abstract: The localization theorem in algebraic topology is a powerful
tool which provides information about the equivariant cohomology of a
space in terms of the fixed point set of the action. It turns out that
this sort of techniques can also be applied to obtain information
about Floer homologies in low-dimensions (which are topological
invariants generally very challenging to compute) leading to
interesting results in topology and geometry. I will discuss
background concepts, motivating questions, and applications; I will
conclude by describing a concrete computation (joint work with M.
Miller Eismeier) of the localization of some of these Floer homologies
in terms of the classical intersection ring of the manifold.
Abstract: Let $C$ be an algebraic curve over $\mathbb{Q}$, i.e., a 1-dimensional
complex manifold defined by polynomial equations with rational coefficients.
A celebrated result of Faltings implies that all algebraic points on C come in families of
bounded degree, with finitely many exceptions. These exceptions are
known as isolated points. We explore how these isolated points behave
in families of curves and deduce consequences for the arithmetic of
elliptic curves. This talk is on joint work with A. Bourdon, Ö. Ejder, Y. Liu, and F. Odumodu.
If you have any questions or concerns do not hesitate to contact us at: gta[dot]temple[dot]math[at]gmail[dot]com.
You can also contact the individual graduate organizers: