November 10-11, 2007
Algebraic and Geometric Topology Conference in honor of Bob Stong
http://www.math.virginia.edu/StongConf

Thursday, October 25, 2007, 4:00pm
Location: Kerchof 317
Title: Interrogating Emergent Properties of Biochemical Networks TBA
Jason Papin (UVA, Department of Biomedical Engineering)
The reconstruction and mathematical analysis of genome-scale biochemical networks is a pressing challenge for making the connection between genotype and phenotype of biological systems. Three topics will be discussed: (1) the development of novel computational approaches for interrogating properties of mathematical representations of these networks; (2) the discovery of fundamental biology with these systems-level models; and (3) the application of such network analysis tools to address clinical problems. These network reconstructions and analyses facilitate the integration of high-throughput datasets to characterize properties that arise from the biochemical networks and are thus beginning to drive fundamental discoveries in biology.
(Refreshments precede the talk at 3:30pm in Kerchof 314)

October 14, 2007
Symposium in honor of Loren D. Pitt
http://www.math.virginia.edu/PittSymposium/

Thursday, October 11, 2007, 4:00pm
Location: Kerchof 317
Title: How Large Asexual Populations Adapt
Michael Desai (Princeton)
We often think of beneficial mutations as being rare, and of adaptation as a sequence of selected substitutions: a beneficial mutation occurs, spreads through a population in a selective sweep, then later another beneficial mutation occurs, and so on. This simple picture is the basis for much of our intuition about adaptive evolution, and underlies a number of practical techniques for analyzing sequence data. Yet many large and mostly asexual populations---including a wide variety of unicellular organisms and viruses---live in a very different world. In these populations, beneficial mutations are common, and frequently interfere or cooperate with one another as they all attempt to sweep simultaneously. This radically changes the way these populations adapt: rather than an orderly sequence of selective sweeps, evolution is a constant swarm of competing and interfering mutations. I will describe some aspects of these dynamics, including why large asexual populations cannot evolve very quickly and the character of the diversity they maintain. I will explain how this changes our expectations of sequence data, how sex can help a population adapt, and the potential role of "mutator" phenotypes with abnormally high mutation rates. I will also describe ways to study these dynamics directly using experimental yeast populations.
(Refreshments precede the talk at 3:30pm in Kerchof 314)

Thursday, September 27, 2007 7:30pm
Location: Gilmer Hall 190
Mathematics, Preferences, and Voting in Agreeable Societies
Francis Edward Su (Harvey Mudd College)
Free lecture for a general audience.

Those attending the talk may wish to park near the UVa football stadium.
Gilmer is building #17 on the map at:
http://www.virginia.edu/webmap/GMcCormickRoadArea.html
and building #9 at:
http://www.virginia.edu/webmap/HStadiumHereford.html

When mathematical objects have a social interpretation, the associated theorems have social applications. We give examples of situations where sets model preferences, and suggest extensions of classical theorems on convex sets which have applications to the analysis of voting in "agreeable" societies. When do majorities exist? How does the shape of the political spectrum influence the outcome? What does mathematics have to say about how people behave? No advanced background in mathematics is assumed.

Francis Edward Su is a Professor of Mathematics at Harvey Mudd College. He earned his Ph.D. from Harvard University, and has held visiting positions at Cornell and MSRI. His research is in topological and geometric combinatorics and applications to the social sciences, and he has co-authored nearly a couple dozen papers with undergraduates. He also has a passion for teaching and popularizing mathematics.

From the Mathematical Association of America, he received the 2001 Merten M. Hasse Prize for expository writing, the 2004 Henry L. Alder Award for distinguished teaching, and was the 2006 James R. C. Leitzel Lecturer. He also serves on editorial boards of the American Mathematical Monthly and Math Horizons. In his spare time he enjoys working on his "Math Fun Facts" website, which receives nearly 4,000 hits every day.

Thursday, September 27, 2007 4:00pm
Location: Kerchof Hall 317
Combinatorial Fixed Point Theorems and Fairness
Francis Edward Su (Harvey Mudd College)
Refreshments served at 3:30 in Kerchof Hall Common Room (314)

The Brouwer fixed point theorem is a well-known classical theorem in topology with important applications. Less well-known is an equivalent combinatorial formulation known as Sperner's lemma. We survey some recent applications of variants and relatives of Sperner's lemma, including an extension to polytopes and combinatorial equivalents of other topological theorems. These have some striking applications in "fair division" problems in mathematical economics: cake-cutting, rent-splitting among housemates, and resource allocation. Proofs exhibit interesting connections between combinatorics, topology and the social sciences. Research with undergraduates has played a big role.

Thursday, March 29 2007 4:00pm
Location: Kerchof 317
Explorations of Cancer Genomes: Mutation, Permutation, and Duplication
Ben Raphael (Brown University, Department of Computer Science & Center for Computational Molecular Biology)
Refreshments precede talk at 3:30pm in Kerchof 314.
Cancer is a disease driven by selection for somatic mutations that alter the structure, function or regulation of genes. These mutations range from single letter changes in DNA to rearrangements, gains, or losses of large pieces of DNA. In some types of cancer these large-scale alterations are directly implicated in cancer development and provide targets for cancer diagnostics and therapeutics. The study of mutation in cancer genomes is presently exploding as a result of the sequencing of the human genome and new experimental technologies that enable high-resolution analysis of cancer genomes. I will describe the computational and mathematical challenges that arise in these studies. The main focus will be on the analysis of data from two experimental techniques that measure large-scale alterations in cancer genomes: End Sequence Profiling (ESP) and array comparative genomic hybridization (aCGH). Modeling of this data using methods inspired from phylogenetics reveals a parsimonious sequence of rearrangements that transform the normal human genome into a cancer genome. However, the data suggests more complicated patterns of overlapping rearrangement and duplication events that require new models. I will discuss one such model, duplication via amplisome, and survey future directions.