# Seminars and Colloquia

## Other

Apr 12

#### Mathematics Colloquium

04:20 pm

Aaron Brown, University of Chicago Recent progress in the Zimmer program Abstract: The Zimmer program refers to a number of questions and conjectures about actions of certain discrete groups, namely, lattices in higher-rank simple Lie groups. The primary example example of a such a group is SL(n,R). In the past few years, there has been significant progress in the Zimmer program. In my talk, I will discuss a recent proof of Zimmer's conjecture which shows that (cocompact and certain non-uniform) higher-rank lattices do not act on manifolds with low dimension. I will also discuss recent results and work in progress that classify all possible non-trivial actions under certain dynamical or dimension assumptions.

Nov 30

#### PCSE/IDEAS: Programmers Summit

12:00 pm

By invitation only. Contact mjkingsley@wesleyan.edu to learn more.

Nov 10

#### KrisTapp Talk

12:00 pm

Wesleyan's Undergrad Math Club Presents: The Math of Gerrymandering Abstract:In Gill v. Whitford , a Wisconsin court struck down the state assembly map as unconstitutional gerrymandering. Will the US Supreme court uphold this landmark ruling? The plaintiffs case hinges on elementary mathematics, including a simple new efficiency gap formula that attempts to measure gerrymandering. For deciding whether this formula works, a few highly relevant mathematical facts were discovered so recently, the Supreme Court probably doesnt know about them. But you will if you attend this talk. No math or political science background will be assumed.

Nov 8

#### Computer Science Open House

12:00 pm

Nov 1

#### Mathematics Open House

12:00 pm

Oct 26

#### Ann Guo Talk

12:00 pm

Wesleyan's Undergrad Math Club Presents: Ann Guo Career Engineering 101 Come learn how to design, build, and test careers that will fulfill your passions while considering the limitations imposed by parents, society, and studentloans. Ann is an MIT-trained computer scientist who eventually found her calling as a career coach. In between, she ran global campus recruiting at analgorithmic trading firm where she gained insider knowledge on the hiring process. At Passion Analytics, she is developing an automated online careercoach to help people at scale. Ann holds BS & MEng degrees in Computer Science from MIT and PhD from UMass Amherst. Lunch will be served!

Oct 22

#### MAMLS Conference

09:00 am

The Mid-Atlantic Mathematical Logic Seminar, supported by the NSF, will start its 2017-2018 season at Wesleyan University. 8 distinguished researchers will give 50-minute lectures, many on model theory, over the course of a day and a half. Day 2 Schedule: 9-9:50: Alexandra Shlapentokh, "The Definability World in Number Theory." 10:30-11:20: Philipp Rothmaler, "Pure submodules of direct products of finitely presented modules." 11:30-12:20: Deirdre Haskell, "Residue field domination in theories of valued fields."

Oct 21

#### MAMLS Conference

09:00 am

the Mid-Atlantic Mathematical Logic Seminar, supported by the NSF, will start its 2017-2018 season at Wesleyan University. 8 distinguished lecturers will give 50-minute lectures, many on model theory, over the course of a day and a half. Day 1: 9-9:50: Alex Kruckman, "Generic theories, independence, and NSOP1." 10:30-11:20: Sergei Starchenko, "The topological closure of algebraic and semi-algebraic flows on complex and real tori." 11:30-12:20: Hans Schoutens, "Defining affine n-space." 2:30-3:20: Alice Medvedev, "Feferman-Vaught and the Product of Finite Fields." 4-4:50: Pierre Simon, "Finitely generated dense subgroups of automorphism groups."

Mar 8

#### Google Recruiting Event

04:30 pm

Dec 8

#### Class; Math Club Hill

12:00 pm

Wesleyans Undergrad Math Club presents: Professor Cameron Hill Very Large Networks In the last few decades, we have found that many of the most interesting structures and phenomena around can be described as networks. Examples of these include the Internet, the human brain, computer processors/chips, and many others. So, a network is a just system of discrete elements with connections/interactions between them. When investigating a very large network (e.g. the human brain has something like a hundred billion neurons), it is infeasible to examine each node individually, and even ``looking at the whole network at once is either impossible or basically meaningless. In this situation, we have to settle for examining either ``global processes on the network (which sort of, kind of, allow calculus to make sense) or random local sampling. These options raise several questions like, ``When can we guarantee that random local sampling is not lying to us? and ``Does random local sampling secretly have something to do with global processes? In this talk, I will make some of this stuff a bit more formal and principled, and I will try to explain how we are beginning to address and settle these questions.

Sep 28

#### Wesleyan CS Club - First Meeting

07:00 pm

The Wesleyan CS Club is having its first official meeting of the semester. We'll be talking about hackathons, projects and summer internships! Old and new members are welcome to attend. Non CS majors also extremely welcome. Wednesday 28th September , ESC 339. 7pm .

Apr 15

#### Mini-course in Mathematics: Dave Witte Morris (University of Lethbridge, Canada)

01:10 pm

TALK #1: What is an arithmetic group? Wednesday 4/13 Exley 121 4:15pm-5:15pm ABSTRACT: We will discuss a few basic properties of "arithmetic groups,'' which are certain groups of matrices with integer entries. By definition, the subject combines algebra (group theory and matrices) with number theory (the integers), but it also has connections with other areas, including the theory of periodic tilings. The three talks in this series are almost entirely independent of each other, so it will be perfectly feasible to attend any subset. ------------------------------------------------------------ TALK #2: Some arithmetic groups that cannot act on the line Thursday 4/14 Exley 121 4:15pm-5:15pm ABSTRACT: It is known that finite-index subgroups of the arithmetic group SL(3,Z) have no (orientation-preserving) actions on the real line. This naturally led to the conjecture that most other arithmetic groups also cannot act on the line. This problem remains open, but it can be solved in cases where every element of the group is a product of a bounded number of elementary matrices. No familiarity with arithmetic groups will be assumed. ------------------------------------------------------------ TALK #3: What is an amenable group? Friday 4/15 Exley 121 1:10pm-2:10pm ABSTRACT: Amenability is a fundamental notion in group theory, as evidenced by the fact that it can be defined in more than a dozen different ways. A few of these different definitions will be discussed, and we will see how amenability arises in the study of arithmetic groups. To learn more about arithmetic groups (and the role played by amenable groups), download a free copy of the speaker's book from http://arxiv.org/src/math/0106063/anc/

Apr 14

#### Mini-course in Mathematics: Dave Witte Morris (University of Lethbridge, Canada)

04:15 pm

TALK #1: What is an arithmetic group? Wednesday 4/13 Exley 121 4:15pm-5:15pm ABSTRACT: We will discuss a few basic properties of "arithmetic groups,'' which are certain groups of matrices with integer entries. By definition, the subject combines algebra (group theory and matrices) with number theory (the integers), but it also has connections with other areas, including the theory of periodic tilings. The three talks in this series are almost entirely independent of each other, so it will be perfectly feasible to attend any subset. ------------------------------------------------------------ TALK #2: Some arithmetic groups that cannot act on the line Thursday 4/14 Exley 121 4:15pm-5:15pm ABSTRACT: It is known that finite-index subgroups of the arithmetic group SL(3,Z) have no (orientation-preserving) actions on the real line. This naturally led to the conjecture that most other arithmetic groups also cannot act on the line. This problem remains open, but it can be solved in cases where every element of the group is a product of a bounded number of elementary matrices. No familiarity with arithmetic groups will be assumed. ------------------------------------------------------------ TALK #3: What is an amenable group? Friday 4/15 Exley 121 1:10pm-2:10pm ABSTRACT: Amenability is a fundamental notion in group theory, as evidenced by the fact that it can be defined in more than a dozen different ways. A few of these different definitions will be discussed, and we will see how amenability arises in the study of arithmetic groups. To learn more about arithmetic groups (and the role played by amenable groups), download a free copy of the speaker's book from http://arxiv.org/src/math/0106063/anc/

Apr 13

#### Mini-course in Mathematics: Dave Witte Morris (University of Lethbridge, Canada)

04:15 pm

TALK #1: What is an arithmetic group? Wednesday 4/13 Exley 121 4:15pm-5:15pm ABSTRACT: We will discuss a few basic properties of "arithmetic groups,'' which are certain groups of matrices with integer entries. By definition, the subject combines algebra (group theory and matrices) with number theory (the integers), but it also has connections with other areas, including the theory of periodic tilings. The three talks in this series are almost entirely independent of each other, so it will be perfectly feasible to attend any subset. ------------------------------------------------------------ TALK #2: Some arithmetic groups that cannot act on the line Thursday 4/14 Exley 121 4:15pm-5:15pm ABSTRACT: It is known that finite-index subgroups of the arithmetic group SL(3,Z) have no (orientation-preserving) actions on the real line. This naturally led to the conjecture that most other arithmetic groups also cannot act on the line. This problem remains open, but it can be solved in cases where every element of the group is a product of a bounded number of elementary matrices. No familiarity with arithmetic groups will be assumed. ------------------------------------------------------------ TALK #3: What is an amenable group? Friday 4/15 Exley 121 1:10pm-2:10pm ABSTRACT: Amenability is a fundamental notion in group theory, as evidenced by the fact that it can be defined in more than a dozen different ways. A few of these different definitions will be discussed, and we will see how amenability arises in the study of arithmetic groups. To learn more about arithmetic groups (and the role played by amenable groups), download a free copy of the speaker's book from http://arxiv.org/src/math/0106063/anc/

Apr 11

#### Seminar/Colloquium: Coven/Wood Lecture Series in Mathematics

04:00 pm

Maria Chudnovsky, Professor of Mathematics and PACM at Princeton University "Induced Subgraphs and Coloring" Abstract: The Strong Perfect Graph Theorem states that graphs with no no induced odd cycle of length at least five, and no complements of one behave very well with respect to coloring. But what happens if only some induced cycles (and no complements) are excluded? Gyarfas made a number of conjectures on this topic, asserting that in many cases the chromatic number is bounded by a function of the clique number. In this talk we discuss recent progress on some of these conjectures. This is joint work with Alex Scott and Paul Seymour.

Apr 8

#### Seminar/Colloquium: Coven/Wood Lecture Series in Mathematics

04:00 pm

Maria Chudnovsky, Professor of Mathematics and PACM, Princeton University "Some Problems in Graph Theory" Abstract: In this talk we will survey a few classical problems in graph theory, and explore their relationship to the fields of research that are active today. In particular, we will discuss Ramsey theory, graph coloring, perfect graphs, as well as some more recent research directions.

Nov 10

#### Wesleyan's Undergrad Math Club presents: Professor Karen Collins "Graphs and symmetries"

12:00 pm

Abstract: Many objects in nature have symmetry. Orb web spiders, for instance, create nearly perfect circular webs. Snowflakes have 6-fold radial symmetry, and humans have bilateral symmetry. The set of symmetries of a fixed object form a (mathematical) group, which is a set with a binary relation that is closed, associative, and has an identity element and inverses. Looking at the situation in reverse, every group describes some set of symmetries. Thus, the question arises: for any finite group G, is there an object whose group of symmetries is G? We will answer this question using tools from graph theory.

Jun 3

#### New England Programming Languages and Systems Symposium

09:00 am

NEPLS, the New England Programming Languages and Systems Symposium Series, is a regional venue to discuss current research in programming languages and systems.

May 5

#### Ph.D. Thesis Defense, Gabriel Valenzuela : 'Homological algebra of complete and torsion modules.'

04:15 pm

Abstract: Let R be a Noetherian regular local ring with maximal ideal 𝔪. The category of 𝔪-adically complete R-modules is not Abelian, but it can be enlarged to an Abelian category of so-called L-complete modules. This category is an Abelian subcategory of the full category of R-modules, but it is not usually a Grothendieck category. It is well known that a Grothendieck category always has a derived category, however, this is much more delicate for arbitrary Abelian categories.In this talk, we will show that the derived category of the L-complete modules exists, and that it is in fact equivalent to a certain Bousfield localization of the full derived category of R. L-complete modules should be dual to 𝔪-torsion modules, which do form a Grothendieck category. We make this precise by showing that although these two Abelian categories are clearly not equivalent, they are derived equivalent. As an application, we will explain how this result can be used to effortlessly recover well known duality theorems currently found in the literature.

May 1

#### Masters Thesis Defense, Nick Treuer: 'The Prime Number Theorem and the Riemann ZetaFunction'

02:15 pm

Abstract: Let (x) be the number of primes less than or equal to x. The Prime number Theorem states that (x) asymptotically approaches x=log(x) as x approaches infinity. Using Riemann's zeta function and methods of complex analysis, I will outline a proof of the Prime Number Theorem and then segue into a discussion of the zeta function's analytic continuation to the entire complex plane and the Riemann Hypothesis. I will conclude by very briefly outlining Hardy's 1914 proof that the zeta function has infinitely many zeros on the line Re(s) = 1/2.

Apr 30

#### Anna Haensch (Duquesne, Wes PhD '13): 17 Weird Facts About Science Writing That Will Blow You Away'

04:30 pm

Abstract: A group of scientists make a discovery. We can probably all agree that the world deserves to hear about their work, and we can probably also agree that the scientists deserve some recognition. But how does that science make it from the lab bench to the Twitter feed? And what is the likelihood that the information you eventually consume will be intact, interesting, and accurate? As a mathematician with a background in radio, blogging, social media, and podcasting, I will attempt to answer these questions, and more. I will discuss the evolution of a science story from beginning to end, and like much click-bait, this talk might not actually blow you away -- but then again, maybe it will. There's really only one way to find out.

Apr 28

#### Masters Thesis Defense, Nate Josephs: 'Finding Rational Solutions on a Nonsingular Cubic Surface in P^3'

04:15 pm

Abstract: The purpose of this talk is to present a strategy for parametrizing the rational points on a nonsingular, homogeneous cubic surfaces. The particular Diophantine equation I will consider is X^3 + Y^3 + YZ^2 + W^3 = 0. The strategy will be to find a family of singular cubic curves on our hypersurface with which to sweep through rational solutions, not unlike the standard parametrization of the circle. In this talk I will parametrize the unit circle, as well as a cubic curve. I will then give a brief introduction to algebraic geometry. I will define varieties, the central object of algebraic geometry, and explore the ideal-variety correspondence. This discussion will culminate with the statement of the Nullstellensatz. Having introduced the basics of algebraic geometry, I will proceed to explain the strategy with which I found a 2-parameter set of solutions to the aforementioned polynomial.

Apr 23

#### Undergrad Math Club, Keith Conrad (UConn): 'Continued Fractions'

12:00 pm

Abstract: The standard way to represent a number is through its decimal expansion. Decimals are easy to compare (to see which one is larger) and easy to add and multiply. This talk will be about a different way to write a number: its continued fraction expansion. Continued fractions are not easy to add and multiply, but they are far superior to decimals for the task of finding good approximations. For example, the continued fraction expansion of the square root of 2 leads to the rational approximation 99/70, which has just 2 digits in its denominator but approximates the square root of 2 with an error less than 1/10000.Continued fractions have applications to number theory, dynamical systems, hyperbolic geometry, knot theory, cryptography, and even music theory (why are there 12 notes in the Western musical scale?) and the Gregorian calendar (why is there a leap year every fourth year except if the year is divisible by 100 except if the year is divisible by 400?). In this talk we will learn what continued fractions look like, how to compute them, some of their properties, and we'll learn how to answer seemingly unanswerable questions like this: if an unknown fraction is roughly 2.32558, what is it? (The answer is not 232558/100000.)

#### Undergrad Math Club, Keith Conrad (UConn): 'Continued Fractions'

12:00 pm

Abstract: The standard way to represent a number is through its decimal expansion. Decimals are easy to compare (to see which one is larger) and easy to add and multiply. This talk will be about a different way to write a number: its continued fraction expansion. Continued fractions are not easy to add and multiply, but they are far superior to decimals for the task of finding good approximations. For example, the continued fraction expansion of the square root of 2 leads to the rational approximation 99/70, which has just 2 digits in its denominator but approximates the square root of 2 with an error less than 1/10000. Continued fractions have applications to number theory, dynamical systems, hyperbolic geometry, knot theory, cryptography, and even music theory (why are there 12 notes in the Western musical scale?) and the Gregorian calendar (why is there a leap year every fourth year except if the year is divisible by 100 except if the year is divisible by 400?). In this talk we will learn what continued fractions look like, how to compute them, some of their properties, and we'll learn how to answer seemingly unanswerable questions like this: if an unknown fraction is roughly 2.32558, what is it? (The answer is not 232558/100000.)