Since 1988, the Myhill Lecture Series has featured special presentations and lectures by distinguished mathematicians from around the world. The series is named to honor John R. Myhill, Sr., who served as a UB Mathematics professor from 1966 to 1987. Myhill graduated from Harvard University in 1949. His dissertation is titled, *A Semantically Complete Foundation for Logic and Mathematics. *The UB Mathematics John R. Myhill Lecture Series is funded, in part, by the Darwin D. Martin endowment.

**April 23, 24 and 25, 2024: **Join us for the Myhill Lecture Series: Forty Years of Four Manifolds, featuring Tomasz Mrowka (MIT). Since the twin breakthroughs in 1982-83 by Freedman and Donaldson the study of four manifolds has been developing rapidly. Freedman’s work showed that the homeomorphism problem for 4-dimensional manifolds was largely under control provided the fundamental group of the 4-manifold was not too complicated. Donaldson’s surprising applications of the Yang-Mills equations hinted that the situation for smooth structures was more complicated and that the tools for studying 4-manifolds would come from diverse parts of mathematics. These three lectures will survey a number of the developments that occurred in the ensuing 40 years.

Many problems have been resolved during this time. An few of highlights include; existence of exotic differentiable structures on ℝ4, the failure of the h-cobordism theorem in dimension four, the Thom conjecture on minimal genus of surfaces in the complex projective plane, the Weinstein conjecture on existence of closed Reeb orbits in dimension three, the disproof of the triangulation conjecture, ....

**Lecture 1** will focus on setting up the problems and basic questions in 4-manifold topology.

**Lecture 2** will discuss the many tools that have been developed to aid in this study: the Yang-Mills and Seiberg-Witten equations, Ozsváth and Szabó’s Heegaard Floer theory, Embedded Contact Homology and their applications to question in 3- and 4- dimensional topology.

**Lecture 3** will try to sketch where the theory is headed, including the study the diffeomorphism groups of four dimensional manifolds. I hope to make the lectures independent but some things may flow from one lecture to another.

Myhill Lecture Series: Forty years of Four Manifolds

**Tomasz Mrowka (MIT)**

**April 23, 24 and 25, 2024**

**Tuesday, Wednesday, Thursday**

**4:00 P.M. each day**

**250 Mathematics Building UB North Campus**

**SPEAKER BIO:** **Tomasz Mrowka's** research interests focus on problems in differential geometry and gauge theory. His work combines analysis, geometry, and topology, specializing in the use of partial differential equations, such as the Yang-Mills equations from particle physics to analyze low-dimensional mathematical objects. Jointly with Robert Gompf, he discovered four-dimensional models of space-time topology.

A graduate of MIT, Mrowka received the Ph.D. from U.C. Berkeley in 1988 under the direction of Clifford Taubes and Robin Kirby. He joined the MIT mathematics faculty as professor in 1996, following faculty appointments at Stanford and at Caltech (professor 1994-96). He chaired the Graduate Student Committee 1999-02, and chaired the Pure Mathematics Committee, 2004-15. From 2014-2017 he served as Department Head. A prior Sloan fellow and Young Presidential Investigator, Mrowka was selected for a Clay Mathematics Visiting Professorship in 1995.

In 2007 he received the Veblen Prize in Geometry by the AMS, jointly with Peter Kronheimer, "for their joint contributions to both three- and four- dimensional topology through the development of deep analytical techniques and applications." Their book, Monopoles and Three Manifolds (Cambridge University Press) also garnered the 2011 Joseph Doob Prize of the AMS. He was appointed Singer Professor of Mathematics from 2007 to 2017. In 2017, Mrowka received a Simons Fellowship in Mathematics. In 2018 delivered a plenary address at ICM18 in Rio de Janeiro. He is a Fellow of the American Academy of Arts & Sciences (2007) and Member of the National Academy of Sciences (2015). Most recently, he was awarded the 2023 Leroy P. Steele Prize for Seminal Contribution to Research for his joint paper with Peter Kronheimer, ‘Gauge theory for embedded surfaces, I’ published in 1993 in Topology.

- Gigliola Staffilani, 20228/17/23The Myhill Lecture Series 2022,
*"The study of wave interactions: where beautiful mathematical ideas come together"*will be delivered by Dr. Gigliola Staffilani, the Abby Rockefeller Mauzé Professor of Mathematics at MIT. Her research concerns harmonic analysis and partial differential equations, including the Korteweg–de Vries equation and Schrödinger equation. Join us for each lecture in the series, October 5, 6 and 7, from 4:00 to 5:00 p.m., 250 Mathematics Building, North Campus. - Laura DeMarco, 20199/14/22The Myhill Lecture Series 2019,
*"Complex dynamics and arithmetic geometry"*, will be delivered by Dr. Laura DeMarco, Henry S. Noyes Professor of Mathematics at Northwestern University. She earned her PhD in 2002 from Harvard. DeMarco's research is focused on the dynamics of polynomial or rational mappings on algebraic varieties, especially in dimension 1, with the primary goal of understanding notions of stability and bifurcation. Her recent work explores connections between dynamical properties of maps and the arithmetic geometry of the underlying varieties. - Mark Newman, 20189/14/22Myhill Lecture Series 2018 by Dr. Mark Newman,
*Anatol Rapoport Distinguished University Professor of Physics*, Department of Physics and Center for the Study of Complex Systems, University of Michigan. - Guoliang Yu, 20179/14/22Join us for the 2017 Myhill Lecture Series by Guoliang Yu. His lecture series is entitled "Groups, Manifolds, and Higher Invariants of Elliptic Operators".
- Gopal Prasad, 20169/14/22
**Gopal Prasad,**the Raul Bott Professor of Mathematics at the University of Michigan, delivered the prestigious Myhill Lectures on October 18-20, 2016. The lecture series, titled “Number Theory in Geometry,” drew an overflow crowd to Math 250 for the first talk, an introduction to the history of number theory in geometry. - Ciprian Manolescu, 20159/14/22
**Ciprian Manolescu,**Professor of Mathematics at UCLA, presented the Myhill Lecture Series 2014-15. This 3-part lecture series was held in April 2015, and included a reception in honor of Professor Manolescu after the first lecture. Manolescu earned his BA from Harvard in 2001. In 2002 he won the Morgan Prize for undergraduate research. He continued at Harvard, earning his PhD in 2004 under the supervision of Peter Kronheimer. - Percy A. Deift, 20149/14/22
**Professor Percy A. Deift**from Courant Institute of Mathematical Sciences, NYU, presented the Myhill Lecture Series 2013-14. This 3-part lecture series was held in the Fall, and included a reception in honor of Professor Deift after the first lecture. - Peter Sarnak, 20139/14/22
**Professor Peter Sarnak**from Princeton University presented the Myhill Lecture Series 2013. This 3-part lecture series was held in the Spring, and included a reception in honor of Professor Sarnak after the first lecture.

**Victor Kac** (MIT) November 1988

**David Saltman** (U. of Texas, Austin) February 1989

**Cameron Gordon** (U. of Texas, Austin)
*Combinatorial Methods in Knot Theory.* March 1990

**Armand Borel** (IAS),
*L ^{2}-Harmonic Forms and Topological Invariants*

**Leon A. Takhtajan** (U. of Colorado)
*Geometry and Physics: Uniformization of Riemann Surfaces, Complex Geometry of Moduli Spaces and Two-Dimensional Quantum Gravity.* November 1991

**Ross Street** (Macquarie Univ.) *Categorical Structures in Mathematical Physics and Computing (and Vice Versa).* April 1993

**Peter Kronheimer** (Oxford U. and IAS) March 1994

**Stuart Antman** (U. Maryland)
*Dissipation and Its Delights*. March 1995

**V. Kumar Murty** (U. of Toronto) *
Fermat's Last Theorem, Congruences and L-Functions.* April/May 1996

** DeWitt Sumners** (Florida State University, Tallahassee)

Robert V. Kohn

**William Arveson** (University of California, Berkeley) *Operator Theory and the K-Homology of Algebraic Varieties.* April 2006

** Jonathan David Farley** (University of the West Indies, Jamaica)

Benson Farb

George Papanicolaou

Gopal Prasad

**Guoliang Yu** (Texas A & M University) *Groups, Manifolds, and Higher Invariants of Elliptic Operators*. September 2017

**Mark Newman** (University of Michigan) Lecture 1: *Epidemics, Erdos numbers, and the Internet: The mathematics of networks*; Lecture 2: *Randomized models of networks*; Lecture 3: *Phase transitions and belief propagation in sparse networks. *October 2018.

**Laura DeMarco** (Northwestern University) *Complex dynamics and arithmetic geometry,* September 2019.

**Gigliola Staffilani** (MIT) *The study of wave interactions: where beautiful mathematical ideas come together,* October,2022.

**Tomasz Mrowka** (MIT) *Forty Years of Four Manifolds,* April 2024.

**John R. Myhill, Sr.** (11 August 1923 – 15 February 1987) was a British mathematician. He received his Ph.D. from Harvard University under Willard Van Orman Quine in 1949. He was professor at SUNY Buffalo from 1966 until his death in 1987. He also taught at several other universities. His son, also named John Myhill, is a professor of linguistics in the English department of the University of Haifa in Israel.

Since 1988, the Myhill Lecture Series hosted by UB Mathematics has featured over two dozen distinguished mathematicians from around the world.