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Thursday, April 16, 2026 2:30 pm - 3:30 pm EDT (GMT -04:00)

Algebraic and Enumerative combinatorics seminar - Tyler Dunaisky-Cosmological Correlators and Triangulating the Dual Cosmological Polytope

Speaker:
Tyler Dunaisky
Affiliation: Purdue University
Location: MC 5417

Abstract: A cosmological correlator is an Euler integral, associated to a graph G, which encodes information about the state of the early universe. Evaluation of these integrals is extremely challenging, even in simple cases. However, it turns out the integrand can be identified with the so-called canonical form of the cosmological polytope, revealing a rich combinatorial structure and allowing the application of techniques from commutative algebra. I'll sketch my contribution to this story and advertise the fledgling field of positive geometry, which seeks to generalize the notion of canonical forms to geometric objects more exotic than polytopes.

There will be a pre-seminar presenting relevant background at the beginning graduate level starting at 1:30pm.

Friday, April 17, 2026 10:30 am - 11:30 am EDT (GMT -04:00)

Crypto Reading Group - Maggie Simmons-Formally Verified Correctness Bounds for Lattice-Based Cryptography

Speaker:

 Maggie Simmons
Affiliation: University of Waterloo
Location: MC 6029

Abstract:

Decryption errors play a crucial role in the security of KEMs based on
Fujisaki-Okamoto because the concrete security guarantees provided by
this transformation directly depend on the probability of such an event
being bounded by a small real number. In this paper we present an
approach to formally verify the claims of statistical probabilistic
bounds for incorrect decryption in lattice-based KEM constructions. Our
main motivating example is the PKE encryption scheme underlying ML-KEM.
We formalize the statistical event that is used in the literature to
heuristically approximate ML-KEM decryption errors and confirm that the
upper bounds given in the literature for this event are correct. We
consider FrodoKEM as an additional example, to demonstrate the wider
applicability of the approach and the verification of a correctness
bound without heuristic approximations. We also discuss other
(non-approximate) approaches to bounding the probability of ML-KEM
decryption.
Thursday, April 23, 2026 2:30 pm - 3:30 pm EDT (GMT -04:00)

Algebraic and Enumerative combinatorics seminar - Melissa Ulrika Sherman-Bennett-Dimer face polynomials in knot theory and cluster algebras

Speaker:
Melissa Ulrika Sherman-Bennett
Affiliation: University of California, Davis
Location: MC 5417

Abstract: The set of dimers (aka perfect matchings) of a connected bipartite plane graph G is a distributive lattice, as shown by Propp. The order relation on this lattice comes from the "height" of a dimer, which is a vector of nonnegative integers. In this talk, I'll focus on the dimer face polynomial of G, which is the height generating function of all dimers of G. This polynomial has close connections to knot invariants on the one hand, and cluster algebras on the other. I'll discuss joint work with Mészáros, Musiker and Vidinas in which we explore these connections. No knowledge of knot theory or cluster algebras will be assumed.

There will be a pre-seminar presenting relevant background at the beginning graduate level starting at 1:30pm.