Back to School Seminar (AU '26)
grad students share math they've been up to this summer
Organizer: Bryan Lu (blu17@uw.edu)
Meetings: Fridays 2:30 PM - 3:30 PM @ PDL C-401 or over Zoom
The Back-to-School Seminar invites graduate students to share (mathematical) topics that they find interesting or engage with frequently, similar to the 1-2-3 Seminar that runs in the winter and spring quarters. The intention is to have this seminar bring our graduate student community together after a summer apart and to familiarize incoming first-year students with what older students in the department think about. Speakers are encouraged to share ideas that they’ve recently come across from conferences, reading courses, summer schools, etc. with our community that we might not see otherwise, or share what ideas they’ve been engaging with this summer.
Talks are approximately 51 minutes long and are accessible to a general graduate student audience, i.e. at least \(\frac 1e\) of your talk should be accessible to incoming first-year students.
Schedule
Week 2 – October 9, 2026
Speaker: Zawad Chowdhury
Title: An introduction to expander graphs and HDX
Abstract: How do simplicial complexes and probability theory come together to form a new construction in spectral graph theory, which lets us approximately sample matroid bases and make breakthroughs in complexity theory? Through High Dimensional Expanders (HDX): the construction described above, the hottest new thing in TCS and something I (poorly) learned about this summer. This talk will start with an introduction to spectral graph theory and expander graphs, before giving you a mathematician’s approximate overview of HDX. Come to see how a smattering of mathematical concepts are getting used in TCS, hear what I tell people I do for a living, or learn yet another local-to-global principle!
Week 3 – October 16, 2026
Speaker: Jonas Golm
Title: Enhancing Graph Algorithms Using Vertex and Edge Information
Abstract: Eigenvalues and eigenvectors of matrices associated with graphs relate to features such as connectivity (how easily the graph can be separated), clustering (how nodes form closely connected groups), and network dynamics (how information spreads). How can we integrate the graph’s vertex and edge information into the matrices to enable meaningful analysis? We compare three matrix representations: the standard, weighted, and inner product Laplacians. The standard Laplacian describes networks and connectivity alone, the weighted Laplacian adds connection importance, and the inner product Laplacian offers a simple and transparent way to add node and edge similarity while preserving standard spectral tools. Embeddings and clustering show how node and edge features change network geometry, clusters, and relationships.
Week 4 – October 23, 2026
Speaker: Wolfgang Allred
Title: Diagram Algebras, and the Representation theory of SL2
Abstract: The representation theory of SL2 over the complex numbers is well understood, but what happens in positive characteristic? As one might suspect, it becomes much more difficult. Luckily, there are diagram algebras that can help us in our quest. Along the way, we’ll see what a generalization of Schur-Weyl duality might look like in positive characteristic.
Week 5 – October 30, 2026
Speaker: Varun Shah
Title: Percolation, Subsequences and Combinatorics
Abstract: I am not a probabilist, but I attended an intensive summer school on probability this summer anyway. I’m not quite sure how much I learned, but at least I have something interesting to talk about at the back-to-school seminar! I’ll introduce several famous models and topics in probability, including first-passage percolation, the symmetric exclusion process, and longest increasing subsequences, along with their connections to the Robinson–Schensted–Knuth correspondence and Young tableaux.
Week 6 – November 6, 2026
Speaker: Haocheng Cai
Title: TBA
Abstract: TBA
Week 7 – November 13, 2026
Speaker: Mallory Dolorfino
Title: TBA
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Week 8 – November 20, 2026
Speaker: TBA
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Week 10 – December 4, 2026
Speaker: TBA
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Week 11 – December 11, 2026
Speaker: TBA
Title: TBA
Abstract: TBA