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Notre Dame Math Club

Tentative Schedule of Events
2006-2007

(*DISCLAIMER: None of this has been confirmed and changes WILL be made to this page*)

Colloquia and Seminar Series

Each month the math club will give two talks. The first will be an informational talk designed to speak to undergraduates about some aspect of math in a general sense. As the topics below suggest, these will be very useful talks for students unsure of what they would like to do with math as a career, over the summer, or during the school year. The second talk each month will focus on mathematics. Speakers will include undergraduates, graduate students and faculty members. Topics range from undergraduate research conducted during the summer to cool talks given by students and faculty to show the power and beauty of elementary mathematics. All of these talks will be preceded by tea in the math lounge where students can meet with the speaker and other students. Talks will be late in the afternoon on a Tuesday or Thursday. After the talk, undergraduates are encouraged to head to the dining hall together to eat dinner.

Not listed on the schedule below are the two outside speakers who we expect to talk at Notre Dame. We will have one speaker for the fall semester and one speaker for the spring. These talks will be in addition to the student talks below.

(*Note that the dates will change, they are currently slated as the first and third Thursday of the month*)
DateAbstract
Thursday

September 7th

Being a Math Major at Notre Dame

Thursday September 7th (4pm, Debartolo 126), speakers from the math department and math club will speak about the opportunities for students majoring in mathematics at Notre Dame. Speakers will include Math Professors Frank Connolly, Michael Gekhtman, Matthew Dyer, Steven Buechler and Math Librarian Parker Ladwig.

Topics will include careers in mathematics, student research opportunities, the honors math major and SUMR scholarship, the Putnam Undergraduate Math competition and practice sessions, and library resources. Following the informational meeting, there will be pizza and snacks served in the math lounge and students and faculty are welcome to come and eat.

Thursday
October 5th
The Story of the Poincare Conjecture (5PM Hayes Healy 117)

Speaker: Professor Xiao-Dong Wang, Michigan State University

Abstract: It is well-known that a closed curve is equivalent to a circle topologically. All compact, connected surfaces without boundary are also completely classified. For example, if such a surface is simply-connected (i.e. any closed curves on it are contractible to a point) then it is a sphere topologically. The high dimensional analogues of curves and surfaces are called manifolds. Poincare studied compact, connected 3-manifolds without boundary 100 years ago. As a first step toward classification he conjectured that a simply-connected closed 3-manifold must be a 3-sphere topologically. Hamilton has developed an amazing program to attack the Poincare conjecture and the more general geometrization conjecture using a geometric flow which he calls the Ricci flow. He and others have made remarkable progress. A few years ago Perelman posted 3 papers describing in sketches how to carry out Hamilton's program. Many mathematicians have studied these papers and have been amazed by Perelman's brilliant new ideas. He was awarded the Fields medal by ICM last month. The talk will describe these recent developments and try to convey the flavor of this exciting and active research area. All undergraduate students are welcome to attend this lecture.

Thursday

February 8th

A Crash Course in REUs and Scholarships

Abstract: This event will be a meeting designed for students who think they might be interested in attending an REU in Math this summer. It will include a general discussion of what an REU is, what sort of things should be expected from an REU, what the application process is like, etc. Students who have attended REUs in the past will be there to talk about their experiences and how they enjoyed them. Any student even considering going to an REU is encouraged to come to this meeting to get some useful information and to get a better idea of what and REU is for and how useful it could be. There will be plenty of time provided for any questions you may have, and we will also be joined by Professor Frank Connolly, who will say a few words about the Notre Dame REU. Snacks will be provided.

Thursday

February 1st

Gauss-Bonnet and Foucault

Speaker: Professor Jens von Bergmann

Abstract: There are many links between geometry and physics. This talk explores one that generally does not receive much attention, namely geometric phases. In physics, this term emerged in the mid '80s and encompasses a wealth of phenomena, ranging from Berry's quantum phase, to the Aharanov-Bohm effect, mechanics of deformable bodies, quantum Hall effect, fractional spin, polarized light and the Foucault pendulum. In mathematics, the common link between these phenomena are the concepts of parallel transport and holonomy. In this talk we explain these concepts by focusing in at its core, using the Foucault pendulum on the physics side and the Gauss-Bonnet theorem on the mathematics side. From the mathematics perspective, we will explore basic spherical geometry and prove the Gauss-Bonnet theorem for the round sphere by elementary means. From the physics perspective, we give a geometric explanation of the Foucault pendulum that establishes it as a prototype for a geometric phase. As an application, we show how polarized light in an optical fiber behaves just like a Foucault pendulum. This talk is designed to be accessible to freshmen.

Thursday

April 5th

TO BE DETERMINED

Abstract:

Student Seminars

Date

Title and Abstract

Thursday

September 21st

The Euler Characteristic
4pm, 258 Hurley Hall
Prof. Liviu Nicolaescu

Abstract: The Euler characteristic is an integer naturally associated to a subset of a Euclidean space. It helps to think of it as a sort of "generalized cardinality" since it coincides with the cardinality in the case of finite sets and, just like the cardinality, it satisfies the inclusion-exclusion principle. I will describe its main properties and explain how to use them to compute the Euler characteristic of a set. As an application, I will prove a special case of a theorem of Bernstein-Khovanskii-Koushnirenko which generalizes the classical Bezout theorem. This talk should be accessible to freshmen.

Thursday

February 15th

Faculty Speaker

Abstract:

Thursday

March 29th

Graduate Student Colloquium Talk
Thursday

April 19th

Undergraduate Student Colloquium
Note that this list is just tentative and is more of a list of suggestions than a schedule. The student research talks ideally will contain more than one talk per day. Talks will likely be 20-25 minutes long to allow multiple students to present their research.