**Dr. David Futer (Temple University)**

Friday, September 12, 2014

Mendel Hall, Room 115; 2:30-3:30

**Title: The Rental Harmony Theorem**

The rental harmony theorem (proved by Francis Su a decade ago) is quite possibly the most practically useful theorem that I have come across. Suppose that n housemates are renting a house that has n unequal rooms. The theorem says that under mild hypotheses, there is a way to partition the total rent into rents for the individual rooms, such that every housemate will prefer a distinct room. Furthermore, it provides an algorithm to find this harmonious partition of the rent. I will explain the theorem and its proof.

**Benjamin Seibold (Temple University)**

Friday, September 26, 2014

Mendel Hall, Room 115; 2:30-3:30

**Title: The Analogy of Phantom Traffic Jams and Detonation Waves**

Initially homogenous vehicular traffic flow can become inhomogenous even in the absence of obstacles. Such "phantom traffic jams" can be explained as instabilities of a wide class of second-order macroscopic traffic models. In this unstable regime, small pertubations amplify and grow into nonlinear traveling waves. These traffic waves, called "jamitons", are observed in reality and have been reproduced experimentally. Our research shows that jamitons are analogs of detonation waves in reacting gas dynamics. This analogy enables us to analytically predict the exact shape and travel velocity of the jamitons, by using the Zel'dovich-von Neumann-Doering theory from combustion theory. Moreover, there is an interesting connection between the existence of jamitons, the instability of uniform base states, and a specific "sub-characteristic" condition of the traffic model. Numerical simulations are employed to (a) demonstrate the evolution of small pertubations into fully established detonation waves, and (b) learn about the stability of, and interactions between, jamitons.

Dr. Djordje Milićević, Bryn Mawr College

Friday, September 27, 2013

Mendel Hall, Room 154, 2:45pm (refreshments at 2:30pm)

**Title: Sub_Weyl subconvexity and short p-adic exponential sums**

L-functions are central objects of modern number theory, which guide phenomena ranging from distribution of prime numbers to elliptic curves. One of the principal questions about L-functions is the size of their critical values. Of particular interest are their so-called subconvex estimates, which are deeply arithmetic both in what is required for their proof and in their often spectacular consequences.

In this talk, we will present our recent subconvexity bound for the central value of a Dirichlet L-function of a character to a prime power modulus, which breaks a long-standing barrier known as the Weyl exponent. The results are obtained by developing a new general method to estimate short exponential sums involving p-adically analytic fluctuations. This new theory can be naturally seen as a p-adic analogue of the method of exponent pairs, an essential tool in a wide range of problems in classical analytic number theory. We will present the main results of our method and the key points in its development, and discuss the structural relationship between the p-adic analysis and the so-called depth aspect. This will be a self-contained colloquium talk; no prior familiarity with L-functions or p-adics will be assumed.

**Dr. Elizabeth Beazley, Haverford College**

Friday, September 13, 2013

Mendel Hall, Room 154, 3:15 pm

**Title: The Rim Hook Rule: Enumerative Geometry via Combinatorics**

The theory of quantum cohomology was initially developed in the early 1990s by physicists working in the field of superstring theory. Mathematicians then discovered applications to enumerative algebraic geometry, counting the number of rational curves of a given degree satisfying certain incidence conditions, but the impact now extends into many other aspects of alegebraic geometry, combinatorics, representation theory, number theory, and even back to physics. In this talk, we will explain a "rim hook rule" which provides an efficient way to compute products in the quantum cohomology of the Grassmannian of k planes in complex n-space. This talk will be very concrete and completely self-contained, assuming only a background in basic linear algebra.

Friday, April 12, 2013

**Title: Inverse Problems: Determining the Equation from the Solution**

Mendel Hall, Room 115, 2:30pm

Dr. Shari Moskow, Drexel University

Friday, February 1, 2013

**Title: Modeling and Interpretation of Vaccine Cross-over Clinical Trials Data**

Mendel Hall, Room 115; 2:30 pm

Scott Patterson, Ph.D Senior Director of Statistical Science | Pfizer Vaccine Clinical Research

Friday, September 28, 2012

**Title: The Turn of the Screw: The History and Optimal Design of an Archimedes Screw**

Mendel Hall, Room 154; 2:30 pm

Chris Rorres, University of Pennsylvania and Drexel University

Friday, November 9, 2012

**Title: Stories of Probabilities** **- some (perhaps) non-intuitive results in probability and geometry**

Mendel Hall, Room 154; 2:30 pm

Dr. Charles Grinstead, Swarthmore College

Friday, November 16, 2012

**Title: Unirational Parameterizations of Cubic Surfaces**

Mendel Hall, Room 154; 2:30 pm

Professor Amanda Knecht, Villanova University

Friday, November 30, 2012

**Title: Search Algorithms. **

Tom Corwin, class of '69, founder and CEO of Metron Inc.

Friday, February 11, 2012

**Title: A Two-Parameter Pareto Model for Income Distributions**

Mendel Hall, Room 115 2:30pm

Dr. Klaus Volpert, Villanova University

Friday, April 13, 2012

**Title: Mathematical modeling, transmission dynamics and control of antibiotic-resistant infections
**Mendel Hall, Room 154 2:35

Dr. Mo Yahdi, Ursinus University

Friday, February 3, 2012

**Title: Are you sure that's an ellipse? Poncelet ellipses, Blaschke products, and other mathematical short stories
**Mendel Hall, Room 154 2:35

Dr. Pam Gorkin, Bucknell University

Friday, December 9, 2011

**Title: Complexity and Chaos In Medieval Cartography**

Mendel Hall, Room 154, 2:30 pm

John Hessler, Geography & Map Division, Library of Congress

Friday, November 11, 2011

**Title: Divergence of infinite series on Hecke groups of large width (with a side of Fibonacci)**

Mendel Hall, Room 154, 2:30 pm

Dr. Paul Pasles, Villanova University

Friday, October 28, 2011

**Title: Rational Points on Logical Varieties over Sensible Fields
**Mendel Hall, Room 154, 2:30 pm

Dr. Amanda Knecht, Villanova UniversityFall 2010 - Spring 2011