Advisor: Giulianna Davidoff and Margaret Robinson - Held in Clapp 416: 12:15 pm-1:00 pm, unless noted
Wednesday, February 14, 2018
Title: Independent Studies, Senior Honors Theses, and Summer Research and Internships
Abstract:Learn what faculty do in their research, what opportunities exist for summer research and internships both on- and off-campus. When is an independent study a good idea? What options are there for international students?
Wednesday, February 7, 2018
Speaker: Heather Smith, Georgia Institute of Technology, Atlanta, GA IMPACT Postdoctoral Fellow
Title: Discrete Models for Genome Rearrangement
Abstract: With the natural occurrence of mutations in the genome and the wide range of effects these can incite, scientists seek to understand the evolutionary relationship among current species. Genome rearrangement is a common mode of molecular evolution which naturally lends itself to discrete mathematical models.
While many models have been proposed, there is a need for biologically relevant models which are computationally approachable because the sheer number of evolutionary histories makes it infeasible to check statistics on every possibility. I will introduce three discrete models and survey the state-of-art in computational complexity results surrounding optimal scenarios and phylogenetic trees.
Monday, February 5, 2018 4:00 pm
Speaker: Tarik Aougab, Tamarkin assistant professor of mathematics, Brown University NSF Postdoctoral fellow
Title: The geometry of curve configurations
Abstract: How many loops can be drawn on the surface of a donut so that any two of them cross each other exactly once? What about on a more complicated surface? And what happens if we replace "exactly once" with "at most once", or with "at most some k>1 times"?
There is a countless variety of these questions, all lying at the intersection of topology and combinatorics. Surprisingly, we do not know how to answer even most of the simplest versions. We'll discuss how to solve some of them and we'll describe some deep connections to hyperbolic geometry and group theory.
Friday, February 2, 2018
Speaker: Diana Hubbard, RTG Postdoctoral Assistant Professor, University of Michigan
Title: Knots and their braided representatives
Abstract: If you take a piece of string, tie a knot in it, and glue the two ends of the string together to form a closed loop, the resulting object is what mathematicians call a "knot". Knot theory has connections to many areas of mathematics as well as physics and biology. In this talk I will introduce knots and my favorite way to study them: using the rich and beautiful theory of braids. I will discuss joint work with Peter Feller that addresses, in a large variety of cases, the difficult problem of deciding when a braid representative of a knot is minimal.
Wednesday, January 31, 2018
Speaker: Nicholas Vlamis, RTG Postdoctoral Assistant Professor, University of Michigan
Title: Coloring curves on surfaces
Abstract: A common theme in topology is to try to understand a space through the smaller dimensional spaces that sit inside it. In the case of surfaces (2-dimensional spaces) this means studying circles or loops on the surface. A particularly fruitful way to record this data is through a combinatorial object called the graph of curves. The graph of curves has played a central role in low-dimensional topology in the past two decades. I will introduce this graph and discuss joint work with Jonah Gaster and Josh Greene exploring its structure through its chromatic number, one of the most natural and attractive invariants in graph theory.