Arthur B. Coble Memorial Lectures

This biennial lecture series honors the memory of Arthur B. Coble (1878-1966), Professor of Mathematics at the University of Illinois from 1918 to 1947. The late Professor Coble's family established a fund to endow a series of public lectures on mathematics to be delivered by outstanding mathematicians. The Coble Memorial Lecture series is offered in alternate years with the Tondeur Lecture series.

February 24-26, 2020: Frank Calegari, University of Chicago

Monday, February 24, 2020

4:00 p.m., 314 Altgeld Hall
Title: Digits

Abstract: We discuss some results concerning the decimal expansion of 1/p for primes p, some due to Gauss, and some from the present day. This talk will be accessible to undergraduates.

Tuesday, February 25, 2020

4:00 p.m., 245 Altgeld Hall
Title: Counting
Abstract: What can one say about a system of polynomial equations with integer coefficients simply by counting the number of solutions to these equations modulo primes? We begin with the case of polynomials in one variable and relate this to how the polynomial factors and to Galois theory. We then discuss what happens in higher dimensions, and are led to a conjectural notion of the "Galois group" of an algebraic variety. This will be a colloquium style talk and will be independent of the first talk.

Wednesday, February 26, 2020

4:00 p.m., 245 Altgeld Hall
Title: Coble
Abstract: Coble is known (in part) for his work on invariant theory and the geometry of certain of exceptional moduli spaces in low dimension. We discuss the quest to find explicit equations for one particular family of moduli spaces. An important role is played by a number of exceptional geometrical coincidences and also the theory of complex reflection groups. This will be a colloquium style talk and will be independent of the first two talks.


Previous Lectures

Year Lecturer Lecture Title
1970-71 Irving Kaplansky The Hilbert Problems
1971-72 Samuel Eilenberg Theory of automata
Topology and automata
Categories and automata
1972-73 Derrick Lehmer Unusual Mathematical uses of computers
Some interesting infinite series
Permutation structure and partitions
1973-74 Lipman Bers Some aspects of uniformization
1974-75 Richard Duffin Optimization problems of mathematical science
1975-76 Alonzo Church Set theory with a universal set
1976-77 Andrew M. Gleason Coding theory and combinatorial accidents
1977-78 George W. Mackey Noncommutative harmonic analysis and its applications
1978-79 Saunders MacLane The development of abstract mathematics
Abstract algebra and mathematics today
Possibilities for the future
1979-80 Paul Erdös Recent results and open problems in number theory
Recent results and open problems in combinatorics
Recent results and open problems in set theory
1980-81 Shiing-Shen Chern Exterior differential systems
1981-82 Ron L. Graham Bin packing: A paradigm in the analysis of algorithms
Combinatorial number theory
Euclidean Ramsey theory
1982-83 Richard V. Kadison Non-commutative analysis
1983-84 Jean-Louis Verdier Solitons, symmetries and geometry
1984-85 H. Jerome Keisler Logical areas in probability theory
1985-86 J. William Helton Operator theory, complex variables and optimization problems in electrical engineering
1986-87 Chas. T. Fefferman Mathematical problems of quantum mechanics
1987-88 Wolfgang Schmidt The number of solutions of diophantine equations
A p-adic method in diophantine equations
Quadratic forms and the geometry of numbers
1989-90 Donald A. Martin A chronological survey of Determinacy
1990-91 Burgess J. Davis Lifetimes of conditioned Brownian Motion, and the shapes of the heat kernels
1991-92 Israel Gelfand What is a discriminant and resultant of algebraic equations
A new proof of the oscillation theorem for Sturm-Lionville equations
Cohomology of Poisson algebras
1992-93 Robert Steinberg Central extensions of finite groups, Lie groups, and others
1993-94 Béla Bollobás Projections of bodies and hereditary properties
Oriented percolation in two dimensions
Discrete isoperimetric inequalities
1994-95 Nigel Hitchin Monopoles revised Symmetric Monopoles
The geometry and topology of monopole moduli spaces
1995-96 Kenneth Ribet Fermat's Last Theorem Perfect Powers in arithmetic progression
Component groups and degrees of modular parametrizations
1996-97 Imre Bárány Affine Perimeter and limit shape
On the convex hull of the integer points in a ball
A colourful version of Carathéodory's theorem with applications
1997-98 Freeman Dyson Life in the Universe I. The Paradox of Order and Disorder
Life in the Universe II. The Search for Life
Does the Electron Charge Stay Constant as the Universe Evolves?
1998-99 Yuri Manin
University of Moscow
Quantum Computing
Quantum Cohomology and Mirror Pattern I
Quantum Cohomology and Mirror Pattern II
1999-00 George E. Andrews
Pennsylvania State University
Ramanujan's Lost Notebook
The Rogers-Ramanujan Identities: Some History and Recent Developments
Partitions and Positivity
2000-01 Michael Artin
Noncommutative Algebra in Dimension 2
Noncommutative Projective Surfaces
Orders over Surfaces
2002 Noga Alon
Tel Aviv University and
Institute for Advanced Study
Methods in Modern Combinatorics:
Dimension, Distances, and Information Theory
Polynomials, Addition and Coloring
The Probabilistic Method
2003 Walter Neumann
Columbia University
The Volume of Three-Manifolds
2004 David Eisenbud
Director, Mathematical Sciences Research Institute and
Professor, University of California, Berkeley
Aspects of Elimination Theory:
I. Resultants, from 1693 to now
II. Exterior algebra methods in algebraic geometry
III. Instant elimination, and torsion in symmetric algebras
2005 Peter Sarnak
Princeton University
Zeta functions and spectral theory
2006 Efim Zelmanov
University of California, San Diego
Infinite dimensional Lie (super)algebras
On Golod-Shafarevich groups
Some Ring - Theoretic problems inspired by Combinatorial Group Theory
2007 I.M. Singer
Index Theory: Past, Present, and Future
2008 Ib Madsen
University of Aarhus, Denmark
Moduli Spaces and Topology
2008 Peter Ozsváth
Columbia University
Heegaard Floer homology and knots I and II
Bordered Heegaard Floer homology
2011 Ngo Bao Chau
University of Chicago
Geometry of the Hitchin fibration
2014 Ian Agol
University of California, Berkeley
The virtual Haken conjecture
2016 Sorin Popa
I. Classification of II_1 factors arising from free groups acting on spaces
II&III. Approximating freeness under constraints
2018 Andrea Bertozzi
2020 Frank Calegari
University of Chicago
"Digits" / "Counting" / "Coble"