Can zombie do math?

Skimming through recent book and movie titles, one might imagine that we are headed for a zombie apocalypse. Many have written about what this would entail for our civilization, for our culture, and even for our consumerist tendencies. In this talk we will look at yet another facet of this phenomenon: What would happen to our mathematics? Guided by the history and the philosophy of mathematics, we will pose and search for answers to fundamental questions about the nature of mathematics and how it relates to our humanity.

The Probabilistic Method

Probability theory is a large field in mathematics that, at its core, deals with formulating "uncertainty". Its modern applications range from statistics to economics, from computational biology to finance. But did you know that there are a lot of math questions that seemingly do not involve any probability at all, but a small introduction of uncertainty gives beautiful solutions? This method, known as the probabilistic method, was pioneered by Paul Erdos and is now widely used in many areas of modern mathematics.

Refining Multivariate Value Set Bounds

Speaker: 

Luke Smith

Institution: 

University of California, Irvine, Department of Mathematics

Time: 

Tuesday, June 2, 2015 - 11:00am

Location: 

NS2 1201

Abstract:

Over finite fields, if the image of a polynomial map is not the entire field, then its cardinality can be bounded above by a significantly smaller value. Earlier results bound the cardinality of the value set using the degree of the polynomial, but more recent results make use of the powers of all monomials.

In this talk, we explore the geometric properties of the Newton polytope and show how they allow for tighter upper bounds on the cardinality of the multivariate value set. We then explore a method which allows for even stronger upper bounds, regardless of whether one uses the multivariate degree or the Newton polytope to bound the value set. Effectively, this provides an alternate proof of Kosters' degree bound, an improved Newton polytope-based bound, and an improvement of a degree matrix-based result given by Zan and Cao.

Applying for Math Jobs Workshop

Speaker: 

Dennis Eichhorn

Institution: 

UC Irvine

Time: 

Wednesday, May 20, 2015 - 3:00pm to 4:00pm

Location: 

RH 440R

Getting your PhD in 2016? There are things you should be doing NOW to
plan for your career. In this workshop, we will talk about every aspect
of a successful academic job search in mathematics. This will include

1. Writing a CV, teaching statement, research statement, and cover letter
2. Choosing, cultivating, and asking letter writers
3. Finding job listings
4. Interviewing and negotiating job offers
5. Meeting those early deadlines (and what you need to do by mid-August)

The focus will be on the search for academic jobs, but some resources
regarding the non-academic job search will also be mentioned. All are
welcome, including students that are still years away from finishing.
If you plan to take the job search seriously, there are plenty of things
to start thinking about now that will make you a better job candidate
when you graduate.

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