Mathematics & Computer Science

Seminars and Colloquia

Other

Wednesday, June 03, 2015

09:00 am - 05:00 pm

New England Programming Languages and Systems Symposium

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

ESC 121

Tuesday, May 05, 2015

04:15 pm - 05:30 pm

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

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.

ESC 618

Friday, May 01, 2015

02:15 pm - 04:00 pm

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

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.

ESC 618

Thursday, April 30, 2015

04:30 pm - 05:30 pm

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

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.

ESC 184 (Woodhead Lounge)

Tuesday, April 28, 2015

04:15 pm - 05:50 pm

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

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.

ESC 618

Thursday, April 23, 2015

12:00 pm - 01:00 pm

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

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.)

ESC 109

Thursday, April 23, 2015

12:00 pm - 01:00 pm

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

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.)

ESC 109

Tuesday, April 21, 2015

04:15 pm - 05:15 pm

First Annual Coven-Wood Lecture Series, Bjorn Poonen (MIT): 'How complicated can a field be?'

Abstract: Using ideas from arithmetic geometry, we show how to associate to each countable graph a field in such a way that the automorphism group is preserved. In computable model theory, it was known that countable graphs can encode the complexity of any countable structure. Using our construction, we can now similarly construct countable fields that are as complicated algorithmically as they could possibly be.

ESC 121

Monday, April 20, 2015

04:15 pm - 05:15 pm

First Annual Coven-Wood Lecture Series, Bjorn Poonen (MIT): 'Undecidability in number theory'

Abstract: Hilbert's Tenth Problem asked for an algorithm that, given a multivariable polynomial equation with integer coefficients, would decide whether there exists a solution in integers. Around 1970, Matiyasevich, building on earlier work of Davis, Putnam, and Robinson, showed that no such algorithm exists. But the answer to the analogous question with integers replaced by rational numbers is still unknown, and there is not even agreement among experts as to what the answer should be.

Shanklin 107 (Kerr Lecture Hall)

Friday, April 17, 2015

02:15 pm - 04:00 pm

Honors Talk: Sangsan Warakkagun '15, 'Finite arithmetic subgroups of general linear groups'

Abstract: Let K be a totally real finite Galois extension be the ring of integers in K

ESC 618

Monday, April 13, 2015

04:15 pm - 06:00 pm

Sherman Prize Exam!

Are you a first year student? Do you like math? Do you like a challenge? Then come participate in the Sherman Prize Exam! The Sherman prize exam consists of challenging, but not impossible, math problems. All you'll need is the desire to have fun with math puzzlers, and a pencil. Contact Karen Collins kcollins@wesleyan.edu) if you have any questions. If you can't make the time, we can work something out.

ESC 618

Monday, April 13, 2015

04:15 pm - 06:00 pm

Sherman Prize Exam!

Are you a first year student? Do you like math? Do you like a challenge? Then come participate in the Sherman Prize Exam!

ESC 618

Thursday, February 26, 2015

12:00 pm - 01:00 pm

Undergrad Math Club Presetns Megan Heenehan (ECSU, Wes PhD '13): 'Kd Are You There???'

Abstract: Suppose I have a group of people and I want to know who is a friend of whom. I want to visualize how the people are connected. We can do this by creating a graph in which we have a vertex for each person and we put edges between people who are friends. We can then color the graph by assigning each vertex a color in such a way that if vertices are connected by an edge, that is if people are friends, they are assigned different colors. How many colors will we need? If there is a group of people that are all friends with each other they will each need a different color, this is a clique in the graph. More generally, if there are d people who are all friends with each other then there is a clique of size d (Kd) the graph will require at least d colors. Is the converse true? That is, if we need to use d colors, does this mean there is a clique of size d in the graph? Or are there d people that are all connected in some other way? In terms of graph theory the question is: Does a graph requiring d colors contain a Kd in some way? In this talk we will look at some attempts to answer this question. No prior knowledge of graph theory will be assumed.

ESC 184 (Woodhead Lounge)

Thursday, November 20, 2014

12:00 pm - 01:00 pm

Undergraduate Math Club Presents: Professor David Constantine (Wes) ' The SIR Model and the Ebola Outbreak'

What can mathematics tell us about the Ebola outbreak in West Africa? Can we understand the spread of the disease and make predictions about its course? How can modeling inform the public health response? In this talk, I'll survey the SIR model, a simple but important tool in epidemiology. Using some simple ideas from probabilty, calculus, and differential equations, we'll build a model that has predicted the course of the outbreak very well so far. Then we'll look at some ways we might modify it to make it more accurate and to better reflect the way diseases spread. We'll see what it can tell us about bringing the outbreak under control, about herd immunity, and about why you should get a flu shot. Lunch will be provided!

ESC 109

Thursday, November 13, 2014

12:00 pm - 01:00 pm

Undergraduate Math Club, Professor Karen Collins (Wes): 'The Map-Coloring Game'

Mathematical conjectures which are easy to state but hard to prove can be the most exciting. For example, the Four-Color Theorem (4CT), which states that the regions of any map may be colored with 4 colors so that adjacent regions are colored distinctly, is one of the most famous results in Graph Theory. It was conjectured by F. Guthrie in 1852, given a false proof by A. Kempe in 1879, had its false proof disproved in 1890, and then remained a conjecture until 1976, when it was proved by K. Appel and W. Haken using a computer program that required 1200 hours of computer time. In contrast to the 4CT, it is much easier to show that any map may be 6-colored. In this talk, we will discuss the map-coloring game, which was invented by S. Brams over 30 years ago: Alice wants to color a planar map. She and Bob alternately choose a region to color, using a set of k different colors. Alice wins if the coloring is completed, and Bob wins if it cannot be completed. The game chromatic number of a map is the smallest k such that Alice can win the game on the map. It is fairly easy to show that the game chromatic number of any planar map is less than or equal to 3044, but the largest known value of the game chromatic number is 8. Will it take another 90 years to find the best bound? Lunch will be served!!

ESC 109

Thursday, October 16, 2014

12:00 pm - 01:00 pm

Undergrad Math Club, Brett Smith (PhD Candidate, Wes): Graph Theory and Organized Crime

Abstract: Before his conviction, former American mobster, Joe Massino, famously said, 'there are three sides to every story--mine, yours and the truth.' We explore this idea by asking competing questions: How should you organize a mafia so as not to be caught? How should you patrol a city to disrupt organized crime? Using graph theory and the brilliant work of Robertson and Seymour, we realize that these questions are one and the same and, in the process, develop a powerful notion of connectedness in a network. Unfortunately for ``Big Joey,'' the truth did not set him free. *For anyone who came to the Graduate Speaker Series talk, 'Mine, Yours and the Truth,' this talk will delve deeper into Robertson and Seymour's theory of graph minors, though the focus will still be on grasping the information encoded in treewidth, and no previous knowledge of graph theory will be assumed. Lunch will be provided!!

ESC 109

Thursday, September 25, 2014

12:00 pm - 01:00 pm

Undergraduate Math Club: Constance Leidy (Wes) 'Knots and the Fourth Dimension'

Take a piece of string jumble it up, then seal the ends together. The result is a knot. Notice that you can't untie the knot because you've permanently sealed theends together. (If we don't jumble at all, we'll just end up with a circle, which we call the unknot.) We call two knots equivalent if you can move one jumbled piece of string to look exactly like the other without cutting it open. Knots naturally live in 3-space. We'll discuss a different equivalence relation called concordance involving the fourth dimension. A knot that is concordant to the unknot is called a slice knot. I will discuss some joint work with T. Cochran, S. Harvey, and myself that show that knots in a certain family whose slice status was previously unknown are in fact not slice. Lunch will be provided.

ESC 109

Thursday, September 11, 2014

12:00 pm - 01:00 pm

Undergrad Math Club: What I Did With My Summer Vacation

Come to the year's first meeting of the Undergraduate Math Club! We'll be hearing from five of your fellow students who did math-related research or internships this summer about their work, how they found their programs, and what the experience was like. Their projects included math research here at Wesleyan and at other universities, mathematical biology research, and statistical work at a consulting firm. If you're interested in internships or summer research related to math, or if you just want to hear what some of your fellow students have been up to, be sure to come!Pizza and drinks will be provided!

ESC 184 (Woodhead Lounge)

Monday, April 28, 2014

04:05 pm - 06:00 pm

PhD Defense, James Ricci: 'Finiteness results for regular ternary quadratic polynomials'

Abstract: In 1924, Helmut Hasse established a local-to-global principle for representations of rational quadratic forms. Unfortunately, an analogous local-to-global principle does not hold for representations over the integers. A quadratic polynomial is called regular if such a principle exists; that is, if it represents all the integers which are represented locally by the polynomial itself over ℤp for all primes p as well as over ℝ. In 1953/54, G.L. Watson showed that up to equivalence, there are only finitely many primitive positive definite integral regular quadratic forms in three variables. More recently, W.K. Chan and B.-K. Oh take the first step in understanding regular ternary quadratic polynomials by showing that there are only finitely many primitive positive regular triangular forms in three variables. In this talk, I will give a finiteness result for regular ternary quadratic polynomials in greater generality. By defining an invariant called the conductor and a notion of a semi-equivalence class of a quadratic polynomial, we will utilize the theory of quadratic forms to obtain the following result: Given a fixed conductor, there are only finitely many semi-equivalence classes of positive regular quadratic polynomials in three variables.

ESC 618

Monday, April 14, 2014

04:45 pm - 06:00 pm

Honors Talk, John Treuer '14: On Picard's Theorem

Abstract: Let f be an entire function (that is a complex valued function holomorphic on all of the complex plane). Then if there are two complex numbers that f omits from its range, f must be constant.

ESC 638

Tuesday, February 11, 2014

12:00 pm - 01:00 pm

AIT Budapest Information Session

Come find out about spending time at AIT Budapest studying Computer Science! Pizza will be served!

ESC 184 (Woodhead Lounge)

Saturday, December 07, 2013

10:00 am - 06:00 pm

Putnam Exam

The National William Lowell Putnam Exam will be held this Saturday, Dec. 7th, from 10-1 and 3-6 p.m. in 618 Exley. If you are interested in attending all or part of the exam, please let me know. Six problems are posed in each session, for a total of 12 problems. The modal score on the exam is 0 (out of 120), because the problems are hard, but fun. There is always an elegant way to find the answer, even though it is not obvious at first glance. The topics of the problems range over all kinds of math. Here some examples of Putnam problems: A-2-2000 Prove that there exist infinitely many integers n such that n, n+1, n+2 are each the sum of two squares of integers. A-1-1998 A right circular cone has base of radius 1 and height 3. A cube is inscribed in the cone so that one face of the cube is contained in the base of the cone. What is the side-length of the cube? A-1-1994 Suppose that a sequence a(1), a(2), a(3), ... satisfies 0 < a(n) <= a(2n) + a(2n+1)for all n >= 1. Prove that the series Sum a(n) from n=1 to infinity diverges. A-2-1991 Let A and B be different n x n matrices with real entries. If A^3 = B^3 and A^2B = B^2A, can A^2+B^2 be invertible? Have (math) fun!

ESC 618

Thursday, November 21, 2013

12:00 pm - 01:00 pm

Undergrad Math Club presents a panel on how to use math in everyday life.

A panel discussion on how undergraduate mathematics training prepares someone to use mathematics in their professional life. Panelists include Meredith Hughes, astronomer; Geir Helleloid, software engineer; and David Pollack, mathematician. Questions from the audience will be welcomed. Math club faculty advisors: Collins and Hill.

ESC 184 (Woodhead Lounge)

Thursday, November 07, 2013

12:00 pm - 01:00 pm

Undergrad Math Club: What's Next in Math and Comp Sci?

Wesleyan's Undergrad Math Club presents: What's up next in math and comp sci? How is your math or computer science class going? Interested in taking more? Join us for a discussion of mathematics and computer science course offerings next semester with faculty and majors. Noon, Thursday Nov. 7, Woodhead Lunch will be provided!

ESC 184 (Woodhead Lounge)

Thursday, October 17, 2013

12:00 pm - 01:00 pm

Open House Department of Mathematics and Computer Science

Interested in being a mathematics or computer science major? Then join us for our Open House! Talk to faculty, majors and graduate students. Lunch will be provided!

ESC 184 (Woodhead Lounge)

Saturday, October 05, 2013

08:30 am - 05:00 pm

Discrete Math Days in the Northeast

Speakers will be: Laura Anderson, Binghamton; Andrew Beveridge, Macalester; Dan Cranston, Virginia Commonwealth; Amanda Redlich, Bowdoin; Julianna Tymoczko, Smith

ESC 121

Saturday, October 05, 2013

12:00 pm - 02:00 pm

Discrete Math Days: Poster Session

ESC Lobby (Lawn Ave Side)

Saturday, June 01, 2013

09:00 am - 05:00 pm

Day 2: Conference on Model-Theoretic Algebra in Honor of the retirement of Carol Wood, the Edward Burr Van Vleck Professor of Mathematics

9:30 am John Baldwin: Completeness and Categoricity (in power): Formalization without Foundationalism 10:30 am Daniel Saracino: The 2-color Rado Number of x1+x2+ xm-1 = axm 1:30 pm Zo - Chatzidakis: Some remarks on fluent completions 3:00 pm David Marker: Uncountable Real Closed Fields with PA Integer Parts

ESC 121

Friday, May 31, 2013

03:00 pm - 05:00 pm

Conference on Model-Theoretic Algebra in Honor of Carol Wood, the Edward Burr Van Vleck Professor of Mathematics

3 pm Angus Macintyre; Zero sets of exponential polynomials 4 pm Charles Steinhorn: Some model theory for classes of finite structures

ESC 121

Tuesday, April 23, 2013

12:00 pm - 01:00 pm

Undergrad Math Club: 'Solving Polynomial Equations' with Professor Billy Chan

Abstract: Given a polynomial with integer coefficients in several variables, what are the integers represented by this polynomial? We will explore this question and discuss some other related problems. Lunch will be served!

ESC 121

Monday, April 08, 2013

04:15 pm - 06:00 pm

Sherman Prize Exam!

Are you a first-year student? Do you like Math? Do you like a challenge? Then come and participate in the: SHERMAN PRIZE EXAM! - MONDAY APRIL 8, 4:15 @ 6:30 PM - Exley 109. The Sherman prize exam consists of challenging, but not impossible, math problems. All you'll need is the desire to have fun with math puzzlers, and a pencil. Contact Christopher Rasmussen (crasmussen@wesleyan.edu) if you have any questions.

ESC 109

Tuesday, March 05, 2013

12:00 pm - 01:00 pm

Undergrad Math Club Presents Dan Cranston-VCU: 'A Proof of Bertrand's Postulate'

A proof of Bertrand's postulate. Abstract: Bertrand's Postulate states: For every positive integer n, there is some prime number p with n < p \le 2n. This result was conjectured in 1845 by Joseph Bertrand, who verified it for all n < 3 million, and it was proved five years later by Chebyshev (nearly 50 years before the prime number theorem was proved). I'll present a beautiful proof of this result due to Paul Erd\'os.

ESC 121

Thursday, November 15, 2012

12:00 pm - 01:00 pm

Wes's Undergrad Math Club Presents: David Constantine - Wes 'The backwards world of Minkowski geometry'

We are all familiar with Euclidean geometry, since we walk around in it every day. But making just one small change to Euclidean geometry produces the very strange world of Minkowski geometry, where the distance between distinct points can be zero or even negative, where the triangle equality runs backwards, and where a straight line is the longest path between two points. As it turns out, we should be familiar with Minkowski geometry since it, rather than Euclidean geometry, is actually what we walk around in all day. I'll explain why (spoiler alert: relativity), and we'll see how the backwards triangle inequality implies that if you get bored during my talk you can walk back and forth quickly at the back of the room and it will be over sooner for you.

ESC 184 (Woodhead Lounge)

Tuesday, October 09, 2012

11:30 am - 01:15 pm

Study Abroad in Budapest!

Wanted: Computer Science majors who are not just bright, but Creative-Ambitious-Entreprenuerial! Spend a semester in on of Europe's hotspots of creativity: BUDAPEST, Hungary-Study Abroad with world renowned faculty like Erno Rubik of 'Cube' Rubik of 'Cube' fame - Explore fundamentals of CS and IT and special topices in entrepreneurship, design, computer vision, digital film and computational biology - Benefit from small classess taught in English in a state-of-art campus. Experience Central Europe's rich cultural heritage with your newest best friends (Hungarian students) - and you can also opt to learn the language - For more information and application instructions check out: www/ait-bedapest.com - AIT Information Session and Luncheon at Wesleyan

ESC 184 (Woodhead Lounge)