Seminars10
From CanisiusmathWiki
SEMINAR ANNOUNCEMENTS
6/17 (Thur.), 3:00 -- 4:00 p.m., OM 320.
Speaker: Richard Gustavson (Cornell University)
Title: Circle Packings and Edge Flippings
Abstract: In this talk I define a circle packing and prove that any two circle packings of the sphere with the same number of circles can be transformed from one to the other through a sequence of simple combinatorial modifications called edge flips. After observing that every edge flip has a unique inverse, I develop an algorithm that identifies a sequence of edge flips that transforms any circle packing into a standard, dipole form, then prove that this algorithm performs its intended function.
This is a report from Richard's research last summer. For background, see [1] (http://www.math.utk.edu/~kens/)
6/24 (Thur.), 3:00 -- 4:00 p.m., OM 320.
Speaker: Elizabeth Wicks (University of Washington-Seattle)
Title: A New Tool for Studying Climate Change: The Ice-Penetrating Probe
Abstract: Gathering reliable data about the rapidly shrinking sea ice cover of the Arctic is crucial to the study of climate change. Expanding our knowledge of processes beneath sea ice would expand our knowledge of features that significantly affect the global environment, such as ice thickness, melt rate, and ice and ocean temperatures. Yet we currently have no means of deploying instrumentation beneath sea ice short of landing on the ice and operating it manually, which is not practical for long-term measurements. To meet the demand for long-term data on sub-ice processes, our research team is developing an autonomous ice-penetrating probe. We will use the same deployment method as previous researchers, who have succeeded in deploying instrumentation on the ice surface via airplane. Other researchers have developed electrically powered ice penetrating probes, which were successfully deployed in glaciers on land to depths of hundreds of meters. However, these probes required manual operation and were inefficient because of their large size, which was limited by the size of the electronics available at the time. Advances in technology have greatly reduced the size of the electronics required to make useful measurements, enabling our research team to construct an electrically powered ice-penetrating probe that is smaller, more efficient, and autonomous. We are constructing such a probe by creating and testing a succession of design prototypes that are providing insight into the dynamics of ice penetration. Our successful first test article is faster and more efficient than previous models, penetrating through about 40 centimeters of saline ice at a rate of 6.6 meters per hour with an average power input of 500 watts. The final probe design will be capable of deployment via airplane and will autonomously penetrate through sea ice to reach the ocean beneath, enabling the study of sub-ice processes.
7/1 (Thur.), 4:00 -- 5:00 p.m., OM 320.
Speaker: Dr. Jonathan Lopez (Canisius graduate, PhD from University of Rochester)
Title: Lie algebras constructed from 2x2 matrices
Abstract: We define principal congruence subgroups and show how they can be used to construct a Lie algebra for the case SL(2,Z), i.e., 2x2 matrices with integer coefficients and determinant 1. We will calculate the Lie algebra structure completely, and give a description as a restricted Lie algebra with a finite set of generators. [Aside: Introducing this additional structure allows us to obtain cohomological results about the underlying congruence subgroup in many cases.]
7/8 (Thur.), 4:00 -- 5:00 p.m., OM 320.
Speaker: Kelsey Watson (Valparaiso University)
Title: Medians of Permutations
Abstract: The distance between two permutations can provide insight to situations such as voting and comparing strands of DNA. There are many ways to define the distance between a pair of permutations. We have worked with the distance axioms to define new distances. The Median is a permutation which gives the smallest sum of distances between itself and each permutation in the given set. Given a set of permutations and a distance, d, we are interested in computing the Median(s) of that set. For several different distances we are developing theorems to find how many and what medians a set of permutations and a distance, d, may have.
7/9 (Fri.), 4:00 -- 5:00 p.m., OM 320.
Speaker: Dominic Dotterrer (University of Toronto)
Title: Computing the volume of high dimensional convex bodies
Abstract: I will bound from above the volume of a convex polytope with N vertices contained in an n-dimensional unit sphere. As a corollary, I will discuss the difficulty of algorithmically computing the volume of general convex bodies in high dimensions.
7/15 (Thur.), 4:00 -- 5:00 p.m., OM 320.
Speaker: Dr. Bernard Badzioch (SUNY-Buffalo)
Title: Fair division and measure theory
Abstract: The classical fair division problem ask how one can divide a cake among n people in a fair manner. I will explain a solution of this problem due to Banach and Knaster, and how it gives rise to a theorem in measure theory.
7/16 (Fri.), 4:00 -- 5:00 p.m., OM 320.
Speaker: Dr. Seshendra Pallekonda (King's College)
Title: Ideas behind Riemann-Hurwitz bound
Abstract: In this talk, we use unifying ideas from several areas of Mathematics such as Hyperbolic Geometry, Complex functions - Riemann surfaces, Algebraic Topology etc., to sketch the proof of Riemann Hurwitz upper bound on the number of conformal automorphisms of a Compact Riemann Surface of genus > 1.
