Michigan Number Theory Day

Michigan Number Theory Day will be held at MSU on Saturday, October 3, 2026.

Speakers

• Evangelia Gazaki (University of Virginia)

• Daniel Le (Purdue University)

• Jonathan Love (University of Michigan)

• Stefan Patrikis (Ohio State University)

Registration

Please register here by September 19. There is no fee and your registration will help us with planning (especially with ordering enough food for lunch).

Schedule

All talks in C304 Wells Hall. Lunch and coffee breaks in C204.

• 9:30am-10am: Registration

• 10-11am: Daniel Le -  Generic p-restricted crystalline deformation rings in dimension 3

  • Abstract: In 2008, Kisin constructed potentially semistable p-adic Galois deformation rings. This led to many new instances of modularity. Although a detailed understanding of the geometry of potentially semistable deformation rings is crucial for many arithmetic applications, relatively little is known when the Hodge--Tate weights span an interval of length greater than p. In this talk, I will give explicit presentations of three-dimensional crystalline deformation rings over unramified extensions of Qp when the gaps between consecutive Hodge--Tate weights lie between 4 and p-4. The proof combines Kisin--Taylor--Wiles patching, the Emerton--Gee stack, and recent developments in integral p-adic Hodge theory. This is joint work in progress with Tong Liu. 

• 11-11:30am: Coffee break

• 11:30am-12:30pm: Evangelia Gazaki - Surfaces geometrically dominated by products of curves and a conjecture of Colliot-Thelene for zero-cycles

  • Abstract: For a smooth projective variety X over a field k the Chow group CH_0(X) of zero-cycles is a generalization to higher dimensions of the Picard group of a smooth projective curve. When X is a curve having a k-rational point, its Picard group can be fully understood by the Abel-Jacobi map, which gives an isomorphism between the degree zero elements of the Picard group and the k-points of the Jacobian variety of X. In higher dimensions there is still an Abel-Jacobi map, but the situation is much more chaotic. Namely, over large fields like C, R or Qp this map often has an enormous kernel. In this talk we will focus on the case when the variety X is defined over a finite extension of the p-adic field Qp. In this case, a famous conjecture of Colliot-Thelene predicts that the kernel of the Abel-Jacobi map decomposes as a direct sum of a divisible group and a finite group. In this talk I will present joint work with Jitendra Rathore, where we prove that if π : X -->Y is a dominant rational map between smooth projective surfaces and the conjecture is true for X, then it is true for Y . Using this, we give evidence for this conjecture for many new classes of surfaces including geometrically simple abelian surfaces, Fermat surfaces, new classes of K3 surfaces and isotrivial fibrations.

• 12:30-2:30pm: Lunch break

• 2:30-3:30pm: Jonathan Love - Generating endomorphism rings of supersingular elliptic curves

  • Abstract: Given distinct primes p and l, one can construct a so-called supersingular l-isogeny graph, whose vertices correspond to supersingular elliptic curves over an algebraic closure of Fp and whose edges correspond to isogenies of degree l. If we start at E and follow a path of length k in the isogeny graph that returns to E, composing the corresponding isogenies yields an endomorphism of E with degree l^k. We will prove that the full endomorphism ring of E can be generated by walks of explicitly bounded length in this isogeny graph. This project began at a Banff International Research Station workshop in summer 2025 and is joint with Kirsten Eisentraeger, Eyal Goren, Annamaria Iezzi, Harun Kir, Eda Kirimli, Will Mahaney, Jennifer Park, and Maria Sabitova.

• 3:30-3:45pm: Break

•  3:45-4:45pm: Stefan Patrikis - Effective bounds for adjoint Bloch-Kato Selmer groups of Hilbert modular forms

  • Abstract: A special case of the Bloch-Kato conjecture on special values of motivic L-functions leads to the expectation that the Q_p-linear Bloch-Kato Selmer groups attached to the adjoint motive of a motive of pure weight should vanish. In the case of the p-adic Galois representations attached to cuspidal Hilbert modular representations, such a vanishing result has been established in increasing degrees of generality by Wiles, Diamond-Flach-Guo, Kisin, Allen, and Newton-Thorne. Aside from the works of Wiles and Diamond-Flach-Guo, which are based on integral R=T theorems, these results do not yield effective bounds on the analogous torsion Selmer groups, which feature in the refined form of the Bloch-Kato conjecture. The principal difficulty here is our inability to establish integral R=T theorems when, for instance, p is heavily ramified in F or the Hodge-Tate weights of the Galois representation are much larger than the prime p. I will discuss joint work with C. Khare where we revisit the argument of Chapter 3 of Wiles's Fermat paper and prove effective bounds for torsion Selmer groups in rather general Hilbert modular settings. 

Location

Make sure to enter in the C or D wing. Wells Hall C Wing doors in Google Maps. 

619 Red Cedar Road

C304 Wells Hall (C Wing)

East Lansing, MI 48824

Organizers

Organized by Preston Wake of MSU and Charlotte Chan and Kartik Prasanna of University of Michigan.