Welcome to the website for the Fall 2026 iteration of the MIT Geometry & Topology Seminar, organized by Joye Chen, Ayodeji Lindblad, and Tom Mrowka (executive producer). The seminar meets on Mondays from 3:30PM - 4:30PM (50 minutes + questions) in room 449 of MIT Building 2. You can use this link to add all seminar events to your Google Calendar.
September 14. Bob Gompf, The University of Texas at Austin - The universal $\mathbb{R}^4$ and applications.
We will discuss the universal $\mathbb{R}^4$ and universal smoothings more generally. This work was inspired by a 1986 paper of Freedman and Taylor but extends well beyond it. Simplifications of the main proof lead to a simpler definition and stronger results. One application is a 4-manifold for which the diffeomorphism types of its smoothings are as hard to classify as countable graphs (allowing infinite valence) up to graph isomorphism (joint with A. Panagiotopoulos). Another is to determine the compactly supported mapping class groups of a large class of smooth, open 4-manifolds (joint with P. Orson and A. Ray).
September 21. Kyle Hayden, Rutgers University-Newark - Disordered handles and the complexity of h-cobordisms.
How do you measure the distance between exotic smooth structures on the same 4-manifold? One natural measure is the complexity of an h-cobordism between them. In this talk, I will compare several notions of complexity for h-cobordisms and discuss their relevance to studying 4-manifolds up to stable diffeomorphism. The main new ingredient is a surprising connection between the number of critical points on the h-cobordism and the order in which they appear.
September 28. Hokuto Konno, The University of Tokyo - Families 10/8 revisited.
Furuta's 10/8 inequality is a milestone in the applications of Seiberg–Witten theory to 4-dimensional topology, giving a strong constraint on the intersection forms of smooth spin 4-manifolds. A families version of the 10/8 theorem was considered by Baraglia in 2019, but applications of this families version have not yet been extensively explored. We consider a refinement of Baraglia's families 10/8 theorem and investigate what it tells us about the topology of families of 4-manifolds. This is joint work in progress with Yosuke Morita.
October 5. Jiajun Yan, Rice University - Toward a dynamical interpretation of the McKay correspondence via gauge theory.
In this talk, we will present an exposition of the McKay correspondence, in particular, its various proofs and interpretations using different tools. We will then propose a dynamical way to think about this classical result inspired by Morse theory and gauge theory. Time permitting, we will explain in detail how this approach works in the cyclic cases of the McKay correspondence.
October 12. No speaker - Indigenous Peoples’ Day.
October 19. Dave Gabai, Princeton University - Loops of multi-spheres in $\#_k S^2\times S^2$ and pseudo-isotopy.
We discuss how a pseudo-isotopy of $S^4$ induces for some k, a loop of k embedded pairwise disjoint 2-spheres in $\#_k S^2\times S^2$ where the ith 2-sphere is based at the ith $\text{pt}\times S^2$ and how a loop of spheres induces a pseudo-isotopy. We define a non-trivial invariant with values in $\mathbb{Z}_2$ which vanishes on loops homotopic to ones having geometrically dual spheres. Joint work with David Gay and Daniel Hartman.
October 26. Susan Hermiller, University of Nebraska-Lincoln - A tale of several unknotting conjectures.
Unknotting number is a fundamental measure of how complicated a knot is, measuring how far it is from the unknot via crossing changes. Unknotting number is a challenging invariant to compute; a vast array of tools have been applied to its calculation, and many conjectures have grown up around it. In this talk I will discuss several conjectures aimed at simplifying the task of computing unknotting numbers. I will describe how our resolution of one of these conjectures several years ago led us more recently to resolve another as well as make a new conjecture. This is joint work with Mark Brittenham.
November 2. Gheehyun Nahm, Princeton University.
November 9. Richard Bamler, University of California Berkeley.
November 16. Liam Watson, Universiry of British Columbia.
November 23. No speaker - Thanksgiving week.
November 30. Mira Wattal, Boston College.
December 7. Chris Scaduto, University of Miami.
December 14. Dave Auckly, Kansas State University.
Other seminars & past years: