Plenary Speakers at YMC 2026:

Besides the student presentations, we are delighted to have the following distinguished speakers to deliver plenary talks at YMC:

Maria Han Veiga (The Ohio State University) 

Mathematics of generative diffusion models

Abstract: Diffusion probabilistic models have become the state-of-the-art tool in generative methods, used to generate high-resolution samples from very high-dimension distributions (e.g. images). Although very effective, they suffer some drawbacks: 1) as opposed to variational encoders, the dimension of the problem remains high during the generation process and 2) they can be prone to memorization of the training dataset.

In this talk, we first provide an introduction to generative modeling, with a focus on diffusion models from the point of view of stochastic PDEs. Then, we introduce a kernel-smoothed empirical score and study the bias-variance of this estimator. We find improved bounds on the KL-divergence between a true measure and an approximate measure generated by using the smoothed empirical score. This score estimator leads to less memorization and better generalization. We demonstrate these findings on synthetic and real datasets, combining diffusion models with variational encoders to reduce the dimensionality of the problem.

Jean-François Lafont (The Ohio State University)

Geometric and arithmetic aspects of hyperbolic manifolds

Abstract: Hyperbolic manifolds feature a rich interface between geometry, dynamics, and topology. I will start with a brief introduction to hyperbolic manifolds, focusing on the construction of closed hyperbolic manifolds, both arithmetic and non-arithmetic. I will then discuss some recent work on the presence of totally geodesic submanifolds, and how the presence of these is related to the arithmetic structure of the hyperbolic manifold.

Yunus Zeytuncu (University of Michigan-Dearborn)

Shape Matters: From the Riemann Mapping Theorem to the Bergman Projection in Several Complex Variables

Abstract: In one complex variable, the Riemann Mapping Theorem offers beautiful geometric flexibility. The unit disc and unit square are equivalent. In Several Complex Variables, this simplicity breaks down. The unit ball and polydisc are not holomorphically equivalent in higher dimensions. This geometric rigidity raises a natural question: what are the biholomorphic equivalence classes? When two nice domains are biholomorphically equivalent, how does the mapping behave at their boundaries? Can some boundary invariants answer the equivalence question? We will explore this via Fefferman’s 1974 breakthrough, which proved that any biholomorphic map between strictly pseudoconvex domains with smooth boundaries extends smoothly to the boundary. Because solving such geometric problems requires powerful analytic tools, the talk concludes with an accessible overview of the Bergman projection. We will discuss how its analytic properties are intimately tied to the specific geometry of the underlying domain.

Previous YMCs

Lectures of many of the talks below can be found at the YMC Youtube Channel.

2025 Plenary Speakers

• Pamela E. Harris (University of Wisconsin at Milwaukee)
• Ryan Hynd (University of Pennsylvania)
• Cary Malkiewich (Binghamton University)

2024 Plenary Speakers

• Veronica Ciocanel (Duke University)
• Jordan Ellenberg (University of Wisconsin)
• Carl Wang-Erickson (University of Pittsburgh)

2023 Plenary Speakers

• Alejandra Alvarado (Easters Illinois University)
• Loredana Lanzani (Syracuse University and University of Bologna)
• Camen Rovi (Loyola University)

2022 Plenary Speakers

• Jeff Diller (NotreDame University)
• Julia Plavnik (Indiana University)
• Isabel Vogt (Brown University) 

2021 Plenary Speakers

• Federico Ardila (San Francisco State University)
• Marissa Kawehi Loving (Georgia Tech)
• Jose Perea (Northeastern University)
• Lilian Pierce (Duke University)

2020 Plenary Speakers

• Matthew Kahle (Ohio State University)
• Roland Roeder (Indiana University Purdue University at Indianapolis)

2019 Plenary Speakers

• Moon Duchin (Tufts University)
• Sam Payne (University of Texas at Austin)
• Tatiana Toro (University of Washington) 

2018 Plenary Speakers

• Corina Calinescu (NYC College of Technology, CUNY)
• Francis Edward Su (Harvey Mudd College)
• Karen Smith (University of Michigan) 

2017 Plenary Speakers

• Sarah Koch (University of Michigan)
• Alex Kontorovich (Rutgers University)
• Ezra Miller (Duke University)

2016 Plenary Speakers

• Henry Segerman  (Oklahoma State University)
• Ileana Streinu  (Smith College)
• Melanie Wood  (University of Wisconsin, Madison) 

2015 Plenary Speakers

• Marty Golubitsky (Ohio State University)
• Dave Futer (Temple University)
• Svitlana Mayboroda (University of Minnesota) 

2014 Plenary Speakers

• Benson Farb (University of Chicago)
• Ivelisse Rubio Canabal (University of Puerto Rico)
• Amie Wilkinson (University of Chicago)