The mission of the Seminar for Women in Mathematics is to provide a relaxed, supportive and stress-free environment in which women graduate students, advanced undergraduate students, postdocs and faculty in the department can interact. It also provides a place where women may give talks and discuss mathematics at a level accessible to all graduate students.

The speakers for the seminar are female, usually graduate students or postdocs in the mathematics department. Talks range in length from 30 to 50 minutes, and are at the beginning graduate level. Talks may be on any mathematical topic, and need not represent original research.

- August 28:
**Organization meeting**

- September 11:
**Chia-Yen Tsai**

**Title:**Asymptotic translation lengths in the complex of curves.

**Abstract:**In 1981, Harvey introduced the complex of curves C(S) which captures the combinatorial structure of a surface S. There is a natural action of the mapping class group Mod(S) on C(S), hence we can define asymptotic translation lengths of Mod(S) in C(S) equipped with a metric. We will show that the infinimum length goes to zero like 1/g^2. This talk will be accessible to a general audience. (This is joint work with Vaibhav Gadre).

- September 25:
**Uma Ravat**

**Title:**Interaction on VaR(Value-At-Risk) and CVaR(Conditional-Value-At-Risk) risk measures

**Abstract:**The banking industry relies heavily on the VaR to measure risk which though easy to understand has several shortcomings--it is not subadditive, not convex in general, difficult to optimize and does not take into account losses beyond VaR which may be arbitrarily large. On the other hand, CVaR as a risk measure is preferred in the academic circles due to its interesting properties of coherence and the fact that it does take into account losses larger than VaR. Assuming that a trader thinks in CVaR terms, we study how a constraint on VaR imposed by the trading firm gets translated to an interesting and challenging inverse problem and lay down a framework for solving this inverse problem.

- October 9:
**Alexandra Seceleanu**

**Title:**Weak Lefshetz Property-a computational approach

**Abstract:**I will begin by introducing the algebraic counterpart of the famous Lefschetz Property in differential geometry. Then we shall explore some of the tools that are available for algebraists to study the Weak Lefschetz property. I will show how to completely solve the prolem in a particular case. Time permitting, I will illustrate my talk with computations using computer algebra software. This talk will be easily accessible to non-specialists.

- October 23:
**Inmi Kim**

**Title:**Constructions of Gabor dual window

**Abstract:**I'll give you a brief explanation about the Short Time Fourier Transform and some related theorems. Then we'll see the window conditions for being dual windows in Gabor system. If we have some restrictions on our windows, we can get very simplified window condition which is used for my Gabor dual windows constructions in 1-dimension. Also, if time is okay, I'll give you further topics such as higher dimensional constructions and directionally sensitive Gabor elements.

- November 6:
**Kelly Funk**

**Title:**Introduction to Ergodic Theory and Results on Nonrecurrence

**Abstract:**In this talk we will introduce the subject of ergodic theory by going over some basic definitions and examples. Also we will talk about recurrence and nonrecurrence of sequences. This talk should be accessible to most graduate students.

- November 20:
**Isidora Milin**

**Title:**Flexibility and Rigidity in Symplectic and Contact Worlds

**Abstract:**I will begin by introducing some basic notions of symplectic and contact geometry and explain how they arise from considerations in classical mechanics. Nonexistence of local invariants - all symplectic (contact) manifolds are locally "the same" - will be contrasted with a rich theory of global invariants. I'll finish by discussing an amusing theorem of Gromov (and its contact-geometric analogues) - that there is no way for a symplectic camel to go through the eye of a needle.

- December 4:
**Melissa Dennison**

**Title:**The Bow Sequences

**Abstract:**My dissertation research focuses on a family of recursive sequences called the bow sequences, which have the opposite recursion from the Stern sequence. I will give a brief introduction to the bow sequences and their relation to the Stern sequence, and follow with a discussion of several main properties of the bow sequences. I will derive the generating functions for the sequences and give a description of the bow sequences modulo two. This talk will be accessible to all graduate students.

- February 12:
**Victoria Reuter**

**Title:**An Introduction to Continued Fractions

**Abstract:**I will first introduce some basic definitions and notation for continued fractions. Then we will look at some easy applications of continued fractions in the areas of number theory, analysis, and differential equations. This talk will be accessible to a general mathematical audience.

- February 26:
**Mee Seong Im**

**Title:**Basic Intersection Theory for Non-Algebraic Geometers

**Abstract:**We will first compare the intersection multiplicity of a finite number of planar curves at a point in the Euclidean plane versus the ones in the projective plane. Now what happens when two or more polynomials in two variables have a nonconstant factor in common, or how should we understand self-intersection? How do we then count the intersection multiplicity at a point? Does the notion of intersection multiplicity at a point still make sense or should we extend this notion to the intersection multiplicity at a planar curve? What about the intersection multiplicity of a finite number of polynomials in several variables? What conditions should we impose in order to obtain finite nonnegative integer as the intersection number? Is it possible to obtain negative integers as the intersection number? Background in algebraic geometry is not necessary to understand and investigate these questions.

**Dessert Night:**The Spring 2010 Dessert/Appetizer night will be held on March 5 at 7:30 p.m.

*One of the department's most anticipated ongoing traditions (and by far the tastiest).*

- Hand out by Valerie Peterson.

- Supplement material

- 2009 AWM
workshop at Joint Mathematics Meetings.

Twenty women will be selected in advance of the workshop to present their work -- the selected graduate students will present posters. AWM will offer funding for travel and 2 days' subsistence for the selected participants.

- Association for Women in
Mathematics

They offer workshops, and funding. You can request mentor/mentee from their web page. - Institute
of Advance Study-Women and Math

They offer a summer program every year. If you are interested in the topic, you should definitely apply (fully funded). 2009 Program for Women and Mathematics: Geometric PDE. - Mathematical Sciences Research
Institute

They have "Connections for Women" with different topics each year, and it is a friendly environment. - Career
Mentoring Workshop-for women

They are very helpful and friendly. You should look in to it if you are thinking to graduate in two years. Applications for CaMeW 2009 are due May 15, 2009.*(If the link doesn't work, you can just google CaMeW.)* - Institute for Mathematics and Its
Applications

They offer "Career options for women in mathematical sciences" workshop this year. - Department of Mathematics at
UIUC

Address: 1409 W. Green Street, Urbana, IL 61801

Anna