FYRe (First Year Reading Seminar)
newly-freed grad students share the shenanigans they've been up to (SU 25)
Organizer: Bryan Lu (blu17@uw.edu)
Meetings: Fridays 1:00 PM - 1:30 PM, PDL C401
The FYRe Seminar is a UW student seminar for first-year graduate students to briefly share what they’ve been reading/working on with the rest of their cohort. Older graduate students are welcome to come as well!
For speakers: Talks are short (ideally \(\frac 1e\) of an hour, no more than \(\frac 12\)) and are (hopefully) about topics you’re learning about/working on right now! Having a background in the standard core courses should be sufficient to understand at least half of your talk. Presentations need not be polished nor follow any particular format – this is just an opportunity for us to practice talking about math and share with each other!
Schedule
Week 1 – August 1, 2025
Speaker: Juan José Villamarín Castro
Title: Ricci flow on the disc
Abstract: In this talk we will introduce the basic concepts in order to understand the convergence of the normalized Ricci flow on the disk (with positive scalar curvature) to a metric of constant (positive) curvature and totally geodesic boundary. If time permits, we will discuss in further detail the monotonicity formula of the Perelman’s functionals which is an important step in the proof of the convergence.
Week 2 – August 8, 2025
Speaker 1: Varun Shah
Title: Isoperimetric inequalities on the cube and extremal combinatorics
Abstract: A clutter is a family of subsets of a finite set in which none of the sets contains another. Sperner’s theorem states that among all families of subsets of \(\set{1, 2, ..., n}\) the sets of size \(\frac n2\) form the largest clutter. In true combinatorics fashion, we will see a slick proof of this result. We will then systematically study the geometry of the cube and use an isoperimetric inequality to reprove Sperner’s theorem.
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Speaker 2: William Dudarov
Title: Lipschitz Mass Transport
Abstract: Caffarelli’s contraction theorem says that the optimal transport map from a Gaussian to a measure more log-concave than the Gaussian is 1-Lipschitz. This fact can be used to give two-line proofs of classical functional inequalities for strongly log-concave measures. In these proofs, the optimality of the transport map is not necessary, and so one can attempt to generalize Caffarelli’s theorem by considering other transport maps. We discuss recent progress and open problems in this direction.
Week 3 – August 15, 2025
Speaker 1: Wolfgang Allred
Title: Modular representation theory and the stable module category
Abstract: Gather round as I tell a story about how the failure of Maschke’s theorem in positive characteristic leads to the wild world of modular representation theory and cohomological support varieties.
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Speaker 2: Jonas Golm
Title: Structure of Random Graphs
Abstract: We begin with a proof of Chernoff’s inequality and use it to show that the Erdős–Rényi random graph model undergoes a phase transition—from highly irregular to almost regular—when the expected node degree reaches the order of \(\log n\). We conclude with a discussion of other random graph models and the questions they raise.
Week 4 – August 22, 2025
Speaker 1: Connor McCausland
Title: Pipe dreams and Rubey’s lattice
Abstract: Reduced pipe dreams are combinatorial objects that encode some of the algebraic, enumerative, geometric, and probabilistic properties of Schubert and Grothendieck polynomials. In this talk, we will cover the basic properties of pipe dreams, and we will discuss a recent paper by Sara Billey, Clare Minnerath, and myself which shows that the set of reduced pipe dreams for any permutation \(w\) has a natural lattice structure, proving a conjecture of Rubey.
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Speaker 2: Zihong Lin
Title: Fubini-Study metric
Abstract: To rekindle the joy of first-year manifolds, we discuss the Fubini-Study metric. It is the canonical Hermitian metric (“Riemannian metric but complex”) on the complex projective space. We start with a brisk walkthrough of necessary complex-geometric notions. Then we explore several perspectives often omitted in a first introduction to the Fubini-study metric, explaining why the metric is canonical. Representation theory makes a surprising entry as we apply Schur’s lemma to show that it is the unique metric invariant under the unitary group action.