GSCAGT
May 21 - 23, 2021
Virtual (Philadelphia, PA)
Temple University
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.
This event is sponsored by the Department of Mathematics at Temple University and the NSF.
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Diversity, Equity, and Inclusion
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
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 2021 Registration
Title/Abstract Submission
We are no longer accepting titles and abstracts.
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Keynote Speakers
Moira Chas (Stony Brook University)
- Title: Lie Algebras Related to Curves on Surfaces
- Abstract: In the eighties, Goldman discovered two Lie algebra structures on two vector spaces generated by free homotopy classes of closed curves on a surface. In one case, the basis is given by the classes of oriented curves, and in the other, by the classes of unoriented curves. In this talk, we will explain the definition of these Lie brackets, which combines transversal intersection structure with reconnection of curves. We will describe how the algebraic structure then captures minimal intersection structure of curves on surfaces, in particular counting minimal intersections of a general curve with simple curves and showing the central elements are parallel to the boundary. (The proof uses both hyperbolic geodesic geometry and the effect of Thurston earthquakes on angles at intersection points.) In the case of surfaces with boundary, the set of free homotopy classes of closed, oriented curves is in one-to-one correspondence with the set of cyclic, reduced words (in a certain alphabet). We will discuss an algorithm to compute the bracket and how implementation of the algorithm lead us to conjetures (some of which, later on, became theorems) Time permits, we will discuss how the study of these Lie algebras lead to the discovery of String Topology (jointly with Dennis Sullivan)
Shelly Harvey (Rice University)
- Title: When are Links Weakly Concordant to Boundary Links
- Abstract: Knots are circles embedded into Euclidean space. Links are knots with multiple components. The classification of links is essential for understandingn the fundamental objects in low-dimensional topology: 3- and 4-dimensional manifolds since every 3- and 4-manifold can be represented by a weighted link. When studying 3-manifolds, one considers isotopy as the relevant equivalence relation whereas when studying 4-manifolds, the relevant condition becomes knot and link concordance. The nicest of links are called boundary links since they are closest to a knot: they bound disjointly embedded surface in Euclidean space, called a multi-Seifert surface. The strategy to understand link concordance, starting with Levine in the 60s, was to first understand link concordance for boundary links and then to try to relate other links to boundary links. However, this point of view was foiled in the 90's when Tim Cochran and Kent Orr showed that there were links (with all known obstructions vanishing i.e. Miilnor's invariants) that were not concordant to any boundary link. In this work, Chris Davis, Jung Hwan Park, and I consider weaker equivalence relations on links filtering the notion of concordance, called n-solvable equivalence. We will show that most links are 0- and 0.5-solvably equivalent but that for larger n, that there are links not n-solvably equivalent to any boundary link (thus cannot be concordant to a boundary link). This is joint work with C. Davis and J.H. Park.
Diane Maclagan (University of Warwick)
- Title: Tropical Geometry and Tropical Schemes
- Abstract: Tropical geometry is a combinatorial shadow of algebraic geometry that replaces varieties with objects from polyhedral geometry and related combinatorics. In this talk I will introduce this area, and describe some of the applications. I will then explain how commutative algebra over the tropical semiring (addition is minimum, multiplication is addition) enters this world to develop a tropical scheme theory. No background in algebraic geometry will be assumed.
Davi Maximo (University of Pennsylvania)
- Title: The Waist Inequality and Positive Scalar Curvature
- Abstract: The topology of three-manifolds with positive scalar curvature has been (mostly) known since the solution of the Poincare conjecture by Perelman. Indeed, they consist of connected sums of spherical space forms and S^2 x S^1's. In spite of this, their "shape" remains unknown and mysterious. Since a lower bound of scalar curvature can be preserved by a codimension two surgery, one may wonder about a description of the shape of such manifolds based on a codimension two data (in this case, 1-dimensional manifolds). In this talk, I will show results from a recent collaboration with Y. Liokumovich elucidating this question for closed three-manifolds.
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Schedule
Detailed ScheduleAbstracts
Student Talk Abstracts6th Annual GSCAGT Recorded Keynote Talks
Archive
Past years' websites - including lists of participants and titles/abstracts of talks - and keynote talks:
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GSCAGT, 2015 Website
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2nd Annual GSCAGT, 2016 Website
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3rd Annual GSCAGT, 2017 Website
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4th Annual GSCAGT, 2018 Website
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5th Annual GSCAGT, 2019 Website
Contact Us
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:
- Delaney Aydel: delaney.aydel[at]temple[dot]edu
- Katherine Burke: kjburke[at]temple[dot]edu
- Rose Kaplan-Kelly: rose.kaplan-kelly[at]temple[dot]edu
- Ruth Meadow-MacLeod: ruth.meadow-macleod[at]temple[dot]edu