Niven Lectures

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2023-2024 | 2016-2020 | 2010-2015 | all by 2009

20-21 May, 2024

Benson Farb
University of Chicago

Professor Farb will present two lectures, the first intended for an undergraduate audience.

  • Undergraduate lecture : “Polynomials, braids and you”, 4pm, Monday, May 20 in 110 Fenton Hall

    Abstract : Why did we all have to learn the quadratic formula in middle school? Is learning how to find the roots of a polynomial actually useful? Ask Sergei Brin and Larry Page, whose solution of a specific polynomial evolved into a 1.6 trillion dollar company. In this talk I will trace a path through the 5000 year old saga of polynomials, and of how they became a cornerstone of mathematics and physics. I will also describe some of the new ideas mathematicians are using to understand polynomials, including the theory of configuration spaces and braid groups. This talk is intended for any curious person.

  • Colloquium lecture : “Rigidity of moduli spaces and algebro-geometric constructions”, 4pm, Tuesday, May 21 in 110 Fenton Hall

    Abstract : Algebraic geometry contains an abundance of miraculous constructions, from “resolving the quartic” to the 27 lines on a smooth cubic surface to the Jacobian of a genus g curve. In this talk I will explain some ways to systematize and formalize the idea that such constructions are special: conjecturally, they should be the only ones of their kind.

    I will state a few of these (mostly open) conjectures, and describe some methods used to solve some of them (coming from e.g. topology, geometric group theory, complex geometry). These conjectures can be viewed as forms of rigidity (a la Mostow and Margulis) for various moduli spaces and maps between them. They can also be viewed as a call for a “systematic search” for miracles.

    Much of this talk should be understandable to advanced undergraduates.

11-12 May, 2023

Eli Grigsby
Boston College

Professor Grigsby will present two lectures.

  • “Neural networks and boolean functions”, 4pm, May 11 in 128 Chiles Hall

    Abstract : Deep neural networks can drive cars, produce images from text prompts, and write titles and abstracts for math lectures (J/K… or am I?). A major source of their power is their ability to approximate any function on a compact set. I’ll tell you just enough about neural networks to convince you that this is possible, by focusing on a toy result: any boolean function can be modeled by a neural network of sufficiently high complexity.

  • “The topology, geometry, and combinatorics of feedforward neural networks”, 4pm, May 12 in 128 Chiles Hall

    Abstract : I will begin by describing the structure of neural networks and how they learn. I will then advertise one of the theoretical questions animating the field: how does the relationship between the number of parameters and the size of the data set impact the dynamics of how they learn? Along the way I will emphasize the many ways in which topology, geometry, and combinatorics play a role in the field.

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1-5 October, 2020

Mark Goresky
Institute for Advanced Study

Professor Goresky will present two lectures, the first intended for an undergraduate audience.

 

6-7 May 2019

Alison Etheridge
University of Oxford

Professor Etheridge will present two lectures, the second intended for an undergraduate audience.

 

16-17 April 2018

Melanie Matchett Wood
University of Wisconsin

Professor Matchett Wood will present two lectures, the first intended for an undergraduate audience.

 

1-2 May 2017

Sergei Tabachnikov
Penn State

Professor Tabachnikov will present two lectures, the first intended for an undergraduate audience:

 

6-7 April 2016

Cameron Gordon
University of Texas at Austin

Professor Gordon will present two lectures, the first intended for an undergraduate audience:

  • Undergraduate lecture: “Knots”, 4pm, Wednesday, April 6, 2016 in Fenton Hall 110. There will be pizza after the lecture on the second floor of Fenton; undergraduates especially welcome.
  • Colloquium lecture: “Left-orderability of 3-manifold groups”
    4pm, Thursday, April 7 2016 in Straub Hall 145

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27-28 January May 2015

Pavel Etingof
MIT

Professor Etingof will present two lectures, the first of which is intended for undergraduates:

  • Undergraduate lecture: “Representations of quivers and Gabriel’s theorem”, 4pm, Tuesday, 27 January 2015 in Walnut room, EMU. There will be a reception in Fenton 219 immediately after the talk.
  • Colloquium lecture: “Double affine Hecke algebras”, 2pm, Wednesday, 28 January 2015 in Maple room, EMU. After the lecture there will be tea in Fenton 219.

 

3-4 April 2014

Mikhail Kapranov
Yale University

Professor Kapranov will present two lectures, the first of which is intended for undergraduates:

  • Undergraduate lecture: “How simple is the simplex?”, 4pm, Thursday, 3 April 2014 in 166 Lawrence Hall. There will be a reception in Fenton 219 immediately after the talk.
  • Colloquium lecture: “2-dimensional symmetry of homological algebra”, 4pm, Friday, 4 April 2014 in 208 Deady Hall. Before the lecture there will be tea at 3:15 in Fenton 219.

 

13-14 May 2013

Sergey Fomin
University of Michigan

Professor Fomin will present two lectures, the first of which is intended for undergraduates:

  • Undergraduate lecture: “Periodicity of Cluster Transformations”, 4pm, Monday, 13 May 2013 in 208 Deady Hall. There will be a reception in Fenton 219 immediately after the talk.
  • Colloquium lecture: “Cluster Algebras and Invariant Theory”, 4pm, Tuesday, 14 May 2013 in 112 Lillis Hall. Before the lecture there will be tea from 3:15 in Fenton 219.

 

14-15 May 2012

Ravi Vakil
Stanford University

Professor Vakil will present two lectures, the first of which is intended for undergraduates:

  • Undergraduate lecture: “The Mathematics of Doodling”, Monday, 14 May 2012, 4:00 pm in 208 Fenton Hall.
  • Colloquium lecture: “Cutting and Pasting in Algebraic Geometry”, Tuesday, 15 May 2012, 4:00 pm in 208 Fenton Hall.

 

24-25 May 2011

Denis Auroux
University of California, Berkeley

Professor Auroux will present two lectures, the first of which is intended for undergraduates:

  • Undergraduate lecture: “Seeing into the fourth dimension”, Tuesday, 24 May 2011, 4:00 pm in 100 Willamette Hall. Reception to follow in Willamette Hall atrium.
  • Colloquium lecture: “Building 3-manifold invariants by composing correspondences”, Wednesday, 25 May 2011, 4:00 pm in 100 Willamette Hall. Tea from 3:00 pm to 4:00 pm in Willamette Hall atrium.

 

26-28 April 2010

Alexei Borodin
California Institute of Technology

Professor Borodin will present two lectures, the first of which is intended for undergraduates:

  • Undergraduate lecture, “Around Longest Increasing Subsequences”, Wednesday, 26 May 2010, 4:00 pm in 166 Lawrence Hall.
  • Colloquium lecture, “Interlacing Particle Systems”, Friday, 28 May 2010, 4:00 pm in 208 Deady Hall.

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21-22 April 2008

Allen Knutson
UC San Diego

Professor Knutson will present two lectures, the second of which is intended for undergraduates:

  • Colloquium lecture, “The Space of Commuting Matrices, and Statistical Mechanics”, 4pm, 21 April 2008, 208 Deady.
  • Undergraduate lecture (likely to be interesting to graduate students too), “Juggling Patterns and Gaussian Elimination”, noon, 22 April 2008, 301 Deady.

 

11-12 April 2007

Dan Freed
University of Texas at Austin

Professor Freed will present two lectures, the first of which is intended for undergraduates:

  • Lecture 1: “The geometry and topology of Maxwell’s equations”.
    12:00 p.m., Wednesday, 11 April 2007
  • Lecture 2: “Secondary differential-geometric invariants, generalized cohomology, and QCD”
    4:00 p.m., Thursday, 12 April 2007

 

28 March – 1 April 2005

Alexandre Kirillov
University of Pennsylvania

Professor Kirillov will present three lectures, the second two of which are undergraduate lectures:

  • Lecture 1: “A tale on two fractals”
    4:00 p.m., Monday, 28 March 2005, 106 Deady Hall
  • Lecture 2: “Self-similar fractal sets and generalized numerical systems”
    12:00 p.m., Wednesday, 30 March 2005, 229 McKenzie Hall
  • Lecture 3: “Descartes theorem and its generalization”
    4:00 p.m., Friday, 1 April 2005, 106 Deady Hall

 

24-25 May 200

Peter Sarnak
Princeton University and Courant Institute

Professor Sarnak will present two lectures, the second of which is intended for undergraduates:

  • Lecture 1: “The spectrum of the modular surface”
    4:00 p.m., Monday, 24 May 2004, 208 Deady Hall
  • Lecture 2: “Sums of squares”
    12:00 p.m., Tuesday, 25 May 2004, 229 McKenzie Hall

 

14-15 October 2002

John Conway
Princeton University

Professor Conway will present two lectures, the second of which is intended for undergraduates:

  • Lecture 1: “The 219 space groups”
    4:00 p.m., Monday, 14 October 2002, 110 Fenton Hall
  • Lecture 2: “What’s new about polyhedra and polytopes?”
    4:00 p.m., Tuesday, 15 October 2002, 110 Fenton Hall

 

8-10 May 2000

George Andrews
Pennsylvania State University

Professor Andrews will present two lectures, the second of which is intended for undergraduates:

  • Lecture 1: “Some things Ramanujan may have had up his sleeve”
    4:00 p.m., Monday, 8 May 2000, 110 Fenton Hall
  • Lecture 2: “Ramanujan, continued fractions and teaching mathematics”
    4:00 p.m., Wednesday,10 May 2000, 210 Deady Hall

 

26-28 April 1999

David Eisenbud
Director of MSRI and University of California, Berkeley

Professor Eisenbud will present three lectures, the last of which is intended for undergraduates:

  • Lecture 1: “What free resolutions (might) teach us about geometry”
    4:00 p.m., Monday, 26 April 1999, 110 Fenton Hall
  • Lecture 2: “Free resolutions over exterior algebras”
    4:00 p.m., Tuesday, 27 April 1999, 210 Deady Hall
  • Lecture 3: “How to take a walk using a commutative algebra”
    12:00 p.m., Wednesday, 28 April 1999, 210 Deady Hall

 

May 1997

Michael Artin
Massachusetts Institute of Technology

 

June 1996

Persi Diaconis
Stanford University

 

October 1994

Hugh Montgomery
University of Michigan

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