- There will be a welcome panel to answer questions about how to succeed in grad school, how to find an advisor, etc.
- There will be a discussion on what we would like to see in GSS this semester, where we discuss alternatives to hour-long talks (examples: mini-talks, making pictures in LaTeX, etc.), all input is appreciated!
- We will schedule talks for the semester.
- Speaker: Abhishek Gupta
- Title: Formal Groups
- Abstract: Formal groups are mathematical objects used in algebraic number theory and algebraic topology. In this talk, we shall introduce these objects, look at examples and see some applications.
- Speaker: Rose Morris-Wright
- Title: The Clique-cube Complex for Artin Groups
- Abstract: This talk will introduce a new CAT(0) cube complex, called the Clique-cube complex, associated to an Artin group. I will give examples and properties of this complex. I will also outline how, for particular types of Artin groups, this complex can be used to show that the groups are Acylindrically hyperbolic, or that they have trivial centers. No prior knowledge about Artin groups or CAT(0) cube complexes is assumed.
- Speaker: Mac Krumpak
- Title: An introduction to the Seiberg-Witten equations
- Abstract: The Seiberg-Witten equations are a set of partial differential equations on a closed (3 or 4 dimensional) manifold that encode topological information of the manifold. I will explain a simplified version of the equations and some of the invariants that can be extracted from them. A basic understanding of manifolds is assumed.
- Speaker: Alyssa Canelli, Experiential Learning Office
- Title: Introduction to Experiential Learning
- In lieu of a talk, there will be a workshop on experiential learning. This seminar is joint between GSS and MATH 204a: Teaching Practicum. Students who are not enrolled in MATH 204a are still encouraged to attend.
- Speaker: Charles Stine
- Title: The Role of Casson Handles in the 4-Dimensional h-Cobordism Theorem
- Abstract: The h-cobordism theorem of Smale is one of the primary tools used in the classification of smooth manifolds for dimension greater than four. The proof relies heavily on the ability to freely promote immersed disks to embedded ones in these dimensions, a dependence which causes it to fail spectacularly in dimension four. In the 1980's, M. H. Freedman further developed the ideas of A. Casson and proved a topological version of the result for 4-manifolds. In this talk we will be looking at the proof, analyzing how and why if fails in dimension four, and summarizing the ideas of Freedman and Casson which proved the topological version.
- Speaker: Angelica Deibel
- Title: The Nerve of a Random Coxeter Group
- Abstract: The nerve of a Coxeter group is a simplicial complex whose homology gives some information about the cohomology of the group. In this talk, I will introduce random Coxeter groups and give some results about the homology of the nerve of a random Coxeter group.
- Speaker: Job Rock
- Title: Operads (and why 'Symmetric Monoidal Category' isn’t as frightening as it sounds)
- Abstract: Operads were invented by Peter May to further study infinite loop spaces and spectra. While clearly invented for those interested in abstract nonsense, operads may just find a home in your field, too. The definition of an operad requires a symmetric monodical category, which isn’t as frightening as one might first imagine. We’ll go over the more modern definition of an operad as well as some examples and maybe some applications, time permitting. The definitions of category and functor will be assumed as well as very mild familiarity with sets, topological spaces, (abelian) groups, etc.
- Speaker: Duncan Levear
- Title: Mobius inversion and applications
- Abstract: In combinatorics we are sometimes faced with a counting problem where we know the “total answer” (summing over a partially ordered set) but not the “individual answers” (the terms in the sum). An analogy is knowing the integral of a function, but not knowing the values of the function itself. In this analogy, you would solve the problem by taking the derivative, and in the discrete setting the answer is Mobius inversion. In this talk, I will explain how Mobius inversion works for general posets and present some applications. In particular, I will explain the marvelous case of Hyperplane arrangements, wherein the Mobius function happens to count the number of connected components (Zaslavsky’s Theorem).
- Speaker: Shahriar Mirzadeh
- Title: Divergent Trajectories in Homogeneous Spaces and Moduli Space of Translation Surfaces
- Abstract: In this talk, we will discuss the Hausdorff dimension of the set of points with divergent trajectories in certain homogeneous spaces that has applications to Number theory. The talk will be based on the following paper by Kadyrov, Kleinbock, Lindenstrauss, and Margulis: https://arxiv.org/pdf/1407.5310. If time permits, I will discuss some connections to the Hausdorff dimension of divergent orbits in Moduli Space of Translation Surfaces that turned out to be one of the joint projects I have worked on recently: https://arxiv.org/pdf/1711.10542
- Paper(s): https://arxiv.org/pdf/1407.5310, https://arxiv.org/pdf/1711.10542
- Topology and Neuroscience Event