Department of Mathematics and Statistics, Binghamton University hiltonmemorial

2012

2017-01-05T18:20:20-04:00

Lecture to Honor the Memory of Peter Hilton - 2012

Speaker: Guido Mislin, The Ohio State University and ETH Zürich

Title: Bounded Cohomology and Flat Bundles.

Thursday April 19, 2012, Binghamton University, Lecture Hall 9, 3:00pm.

followed by a Reception at 4.30, Club Room of the Events Center, Binghamton University. This is for the whole Binghamton Mathematics Community as well as for our visitors.

Flyer for the lecture

Abstract:

For an n-dimesional vector bundle over an n-manifold M one defines its Euler number. In case of the tangent bundle, this number is equal to the Euler characteristic of M. Conditions on the bundle restrict the possible values of the Euler number. We will be looking at the case of flat bundles (bundles which are induced from the universal covering bundle by a homomorphism from the fundamental group to the general linear group). For flat vector bundles the absolute value of the Euler number is bounded in terms of the simplicial volume of M, a quantity which only depends on the topology of M. In the case of surfaces, this bound leads to a classical result, due to Milnor, stating that the only oriented surface with a flat tangent bundle is the one with Euler characteristic 0, the torus. We will review related facts and generalizations, talk about recent progress and present some open problems surrounding the topic.

2013

2017-01-05T18:20:20-04:00

Peter Hilton Memorial Lecture - 2013

Speaker: Dani Wise, McGill University

Title: From Riches to Raags: Cubes, Groups and 3-Manifolds

Thursday April 18, 2013, Binghamton University, Science 2, Room 144 3:00pm.

followed by a Reception at 4.15, President's Dining Room, Anderson Center, Binghamton University. This reception is for the whole Binghamton Mathematics Community as well as for our visitors.

Flyer for the lecture

Abstract:

Cube complexes have come to play an increasingly central role within geometric group theory, as their connection to right-angled Artin groups provides a powerful combinatorial bridge between geometry and algebra. This talk will describe the developments in this theory that have recently culminated in the resolution of the virtual Haken conjecture for 3-manifolds, and simultaneously dramatically extended our understanding of many infinite groups.

2014

2017-01-05T18:20:20-04:00

Peter Hilton Memorial Lecture - 2014

Speaker: Doug Ravenel, University of Rochester

Title: A Solution to the Arf-Kervaire Invariant Problem

Thursday April 10, 2014, Binghamton University, Science 2, Room 140 3:15pm.

followed by a Reception at 4.30, in The Chenango Room, Binghamton University. This reception is for the whole Binghamton Mathematics Community as well as for our visitors.

Flyer for the lecture

Abstract:

The Arf-Kervaire invariant problem arose from Kervaire-Milnor's classification of exotic spheres in the early 1960s. Browder's theorem of 1969 raised the stakes by connecting it with a deep question in stable homotopy theory. In 2009 Mike Hill, Mike Hopkins and I proved a theorem that solves all but one case of it. The talk will outline the history and background of the problem and give a brief idea of how we solved it.

2015

2017-01-05T18:20:20-04:00

Peter Hilton Memorial Lecture - 2015

Speaker: Ralf Spatzier, University of Michigan

Title: Higher Rank in Geometry and Dynamics - How isometric and hyperbolic behavior force rigidity

Time: Thursday April 23, 2015, 3:00 p.m.
Location: Binghamton University, Science 2, Room 140

followed by a Reception at 4.30, in The President's Reception Room, Anderson Performing Center, Binghamton University. This reception is for the whole Binghamton Mathematics Community as well as for our visitors.

Flyer for the lecture

Abstract:

Higher rank phenomena have led to surprising rigidity results in group theory, geometry and dynamics. Examples start with Margulis superrigidity theorem for lattices in higher rank semisimple Lie groups, followed by the classification of nonpositively curved Riemannian manifolds with lots of flats. In recent years similar phenomena have been found in dynamics, in particular in the classification of hyperbolic actions on tori and nilmanifolds of higher rank Abelian groups and their measure rigidity.

2016

2017-01-05T18:20:20-04:00

Peter Hilton Memorial Lecture - 2016

Speaker: Amie Wilkinson, University of Chicago

Title: Geometry, Lyapunov exponents and rigidity

Time: Thursday April 28, 2016, 3:00 p.m.
Location: Binghamton University, Fine Arts Building, Room 258

The lecture will be followed by a reception at 4.30 p.m. in The President's Reception Room, Anderson Performing Arts Center, Binghamton University. This reception is for the whole Binghamton Mathematics Community as well as for our visitors.

Flyer for the lecture

Abstract:

To each complete Riemannian manifold $M$ is associated a dynamical system – the geodesic flow on the unit tangent bundle $SM$. To what extent are the dynamical properties of this flow wedded to the geometry of $M$? I will discuss some historical highlights, open questions and recent breakthroughs.

2017

2017-02-01T09:18:03-04:00

Peter Hilton Memorial Lecture - 2017

Speaker: Konstantin Mischaikow, Rutgers University

Title: A combinatorial/algebraic topological approach to nonlinear dynamics

Time: Thursday April 27, 2017, 3:00 p.m.
Location: Binghamton University, Fine Arts Building, Room 258

The lecture will be followed by a reception at 4:30 p.m. in The President's Reception Room, Anderson Performing Arts Center, Binghamton University. This reception is for the whole Binghamton Mathematics Community as well as for our visitors.

Abstract:

The current paradigm for nonlinear dynamics was introduced by H. Poincare and explicitly formulated in the language of differential topology by S. Smale and R. Thom. It was developed to analyze physical systems with models given in terms of nonlinear equations and well-defined parameters with the goal of describing the behavior of a typical trajectory at a typical parameter value. The resulting theory is incredibly complex and has led to the understanding of extremely sensitive structures in both phase space (chaos) and parameter space (bifurcation theory).

However, with the advent of radically improving information technologies science is being evermore guided by data-driven models and large-scale computation. In this setting one often is forced to work with models for which the nonlinearities are not derived from first principles and quantitative values for parameters are not known.

With this in mind I will describe an alternative approach formulated in the language of combinatorics and algebraic topology that is inherently multiscale, amenable to mathematically rigorous results based on discrete descriptions of dynamics, computable, and capable of recovering robust dynamic structures. To keep the talk grounded I will discuss the ideas in the context of modeling of gene regulatory networks.

2018

2018-03-30T15:38:38-04:00

Peter Hilton Memorial Lecture - 2018

Speaker: Vaughan Jones, Vanderbilt University

Title: Local scale transformations in one dimension

Time: Thursday April 12, 2018, 3:00 p.m.
Location: Binghamton University, Academic Building A, Room G023

Abstract: In two dimensional conformal field theory, local scaling symmetry means invariance of some kind under conformal transformations. The quantum theory splits into two one dimensional theories called the “chiral halves”. Conformal invariance then gives a projective representation of the the diffeomorphism group (of the line or the circle) on each of the chiral halves. In an attempt to approximate this local scaling invariance we have considered the Thompson groups F and T as approximations to the diffeomorphism groups. Though this does not work perfectly, it has yielded a kind of “topsy turvy” version of chiral CFT including an interesting family of unitary representations of F and T whose coefficients give, among other things, a way to construct all knots and links from elements of F and T, analogous to the standard construction from the braid groups.

2019

2019-01-31T18:10:57-04:00

Peter Hilton Memorial Lecture - 2019

How hard is algebraic topology? Between the constructive and the non.

Speaker: Shmuel Weinberger, University of Chicago
Time: Thursday April 4, 2019, 3:00 p.m.
Location: Binghamton University, Lecture Hall 9
Abstract: In algebraic topology one studies geometric problems and problems of constructing and deforming highly nonlinear functions by means of algebra. If one knows that two maps are homotopic (i.e. can be deformed to one another) because a certain calculation says they both lie in the trivial group, then what has one learned? (A striking example of this is Smale's turning the sphere inside out, which now can be seen after much highly nontrivial effort, on youtube.) The question I shall discuss is how hard is it to understand what the algebraic topologists tell us.

2020

2024-02-22T19:42:52-04:00

Peter Hilton Memorial Lecture - 2020

Cancelled due to COVID

Exotic Smooth Structures on $R^4$

Speaker: Robert Gompf, University of Texas at Austin
Time:
Location: Binghamton University,
Abstract: One of the most surprising discoveries in 4-manifold topology was the existence of smooth manifolds homeomorphic, but not diffeomorphic, to Euclidean 4-space. For fundamental reasons, this phenomenon can only occur in 4 dimensions. We will survey the subject, from its origin to recent developments regarding symmetries of such manifolds.

The lecture will be followed by a reception at 4:15 p.m. in The President's Reception Room, Anderson Performing Arts Center, Binghamton University. This reception is for the whole Binghamton Mathematics Community as well as for our visitors.

2024

2024-04-09T11:12:53-04:00

Peter Hilton Memorial Lecture - 2024

Polygonal Billiards and Dynamics on Moduli Spaces

Speaker: Alex Eskin, University of Chicago
Date: Thursday, April 11, 2024
Time: 3:00pm
Location: Binghamton University, Lecture Hall 009
Abstract: Billiards in polygons can exhibit bizarre behavior, some of which can be explained by deep connections to several seemingly unrelated branches of mathematics. These include algebraic geometry, Teichmuller theory and ergodic theory on homogeneous spaces. The talk will be an introduction to these ideas, aimed at a general mathematical audience.

About the speaker: Alex Eskin earned his doctorate from Princeton University in 1993, under the supervision of Peter Sarnak. He gave invited talks at the International Congress of Mathematicians in Berlin in 1998, and in Hyderabad in 2010. For his contribution to joint work with David Fisher and Kevin Whyte establishing the quasi-isometric rigidity of solvable groups, Eskin was awarded the 2007 Clay Research Award. In 2012, he became a fellow of the American Mathematical Society. In April 2015, Eskin was elected a member of the United States National Academy of Sciences. Eskin won the 2020 Breakthrough Prize in mathematics for his classification of P-invariant and stationary measures for the moduli of translation surfaces in joint work with Maryam Mirzakhani.

The lecture will be followed by a reception at 4:15 p.m. in the Anderson Center Reception Room, Anderson Performing Arts Center, Binghamton University. This reception is for the whole Binghamton Mathematics Community as well as for our visitors.

Please RSVP at the following link: https://forms.gle/VFsDoz71aJ3exQCE8.

For details contact cmalkiew at binghamton dot edu.

2025

2025-02-24T10:11:25-04:00

Peter Hilton Memorial Lecture - 2025

Letting the rank or genus go to infinity can help. Let's do it!

Speaker: Nathalie Wahl, University of Copenhagen
Date: Thursday, March 20, 2025
Time: 3:00pm
Location: Lecture Hall 10, Binghamton University
Abstract: Many objects come in an infinite family: matrices can have as high a rank as we like, surfaces exist for any given genus, configuration spaces can have any number of points, etc. The principle of homological stability is that letting this rank or genus go to infinity can make certain computations easier.

The talk will explain this principle and then proceed to look for useful rank or genus functions where they were maybe not immediately visible. We will consider objects like Thompson groups, paper garlands, or algebraic versions of garlands that will make odd symplectic groups appear.

About the speaker: Nathalie Wahl earned her doctorate from the University of Oxford in 2001, under the supervision of Ulrike Tillmann. Her main research areas are algebraic topology, geometric topology, and homotopy theory. Wahl has been a pioneer in the field of homological stability, and has a particular interest in mapping class groups, loop spaces, string topology, operads, and field theories. In 2008 Wahl won the Young Elite Researcher Award of the Independent Research Fund Denmark. She was elected in 2016 to the Danish Academy of Natural Sciences, and in 2020 to the Royal Danish Academy of Sciences and Letters. She gave invited talks at the International Congress of Mathematicians in 2022, and at International Congress of Women Mathematicians in Hyderabad in 2010. She is currently the director of the Copenhagen Centre for Geometry and Topology, funded by the Danish National Research Foundation.

For details contact cmalkiew at binghamton dot edu.

2026

2026-02-07T16:49:25-04:00

Peter Hilton Memorial Lecture - 2026

Chasing finite shadows of infinite groups through geometry

Speaker: Martin Bridson, University of Oxford
Date: Friday, March 13, 2026
Time: 3:30pm
Location: Alumni Lounge, Old O'Connor Hall, Binghamton University
Abstract: There are many situations in geometry or elsewhere in mathematics where it is natural or convenient to explore infinite groups of symmetries via their actions on finite objects. But how hard is it find these finite manifestations and to what extent does the collection of all such actions determine the infinite group?

In this colloquium, I will sketch some of the rich history of such problems and then describe some of the great advances in recent years. I'll describe pairs of distinct groups that have the same finite images and I'll sketch the proof of some “profinite rigidity results”, i.e. theorems showing that in certain circumstances one can identify an infinite group if one knows its set of finite images.

We'll pay particular attention to groups that arise in 3-dimensional geometry and topology.

About the speaker: Martin Bridson is the Whitehead Professor of Pure Mathematics at Oxford and President of the Clay Mathematics Institute. He is renowned for his work in geometry, topology, and group theory.

Born in the Isle of Man, he was an undergraduate at Oxford and a graduate student at Cornell (PhD 1991). He subsequently held faculty positions at Princeton, Geneva, and Imperial College London. He has also been a visiting professor at Stanford and the EPFL.

His honours include the LMS Whitehead Prize (1999), AMS Steele Prize (2020), and the Royal Society's Wolfson Research Merit Award (2012). A Fellow of the Royal Society (2016), the American Mathematical Society (2015), and Academia Europeae (2020), he was an Invited Speaker at the International Congress of Mathematicians in 2006 and a Plenary Speaker at the European Congress of Mathematics in 2024.

The lecture will be followed by a reception at 4:45 p.m. in the Atrium of Old Champlain Hall. This reception is for the whole Binghamton Mathematics Community as well as for our visitors.

For details contact cmalkiew at binghamton dot edu.

Peter Hilton seminar

2017-05-06T10:30:58-04:00

Peter Hilton seminar

Title: Recollections of wartime codebreaking

We recommend watching this video in Google Chrome or Firefox.

Peter gave this talk at Binghamton University on March 26, 2009.

Thanks to Marco Varisco for the original MP4 video, which we converted to OGG video format.

Peter Hilton Memorial Lecture

2026-02-03T14:46:59-04:00

Peter Hilton Memorial Lecture

About Peter Hilton

Peter Hilton, 1923-2010, was a member of the Binghamton Mathematics Department from 1982 until his death in November 2010. He was an internationally famous member of the mathematical community. His contributions included a major role in the code-breaking operation at Bletchley Park during World War II, where he worked with Alan Turing, and important research contributions to topology, homological algebra, elementary number theory, combinatorics, and polyhedral geometry, as well as mathematics education at all levels. A collection of memoirs by people who knew Peter has been published in the December 2011 issue of Notices of the American Mathematical Society.

Peter gave a talk to the department about his wartime codebreaking. You can watch it here.