MHC Math and Stat Club Talks

Advisor: Giulianna Davidoff and Margaret Robinson - Held in Clapp 416: 12:15 pm-1:00 pm, unless noted

Wednesday, April 18, 2018

Speaker: Emily Castner, Mathematics Major/Music Minor, Class of 2018

Title:  A distance-based method for phylogenetic tree reconstruction using algebraic geometry

Abstract: Joint work with Dr. Joseph Rusinko and Brent Davis at the Winthrop University 2015 REU

This talk will begin with an overview of Emily’s experiences at the Joint Mathematics Meetings.

We present a new method for inferring the evolutionary relationships between species based on their DNA. To test our method, we simulate evolution under various Markov models. Considering the aligned genomes of four organisms at a time, we then reconstruct a phylogenetic quartet tree. We find that more complex models are generally more accurate, but the simplest model is the most computationally feasible.

Wednesday, April, 11 2018

Speaker: Hiro Tanaka, Benjamin Peirce and NSF Postdoctoral Fellow at Harvard

Title:  Morse Theory, or how to see shapes on a rainy day

Abstract:  Morse theory is a tool that allows us to study a shape by understanding the behavior of a single function on that shape. In this talk I’ll illustrate the power of this idea by drawing connections to invariants like the Euler characteristic and homology groups—for instance, we’ll be able to compute the homology of tori of any dimension, the homology of spheres of any dimension, and the Euler characteristics of these shapes. Then, I’ll talk about the beautiful mathematics underlying some of the ideas of Morse theory, focusing on the idea of moduli spaces.

Monday, April 9, 2018

Speaker: Erica Flapan, Pomona College and Editor in Chief of the AMS Notices

Title:  Topological and Geometric Symmetries of Molecular Structures

Abstract: How does a chemist know that a molecule that he or she has synthesized has the desired form?  Most non-biological molecules are too small to see in a microscope or even with the help of an electron micrograph.  So chemists need to collect experimental data as evidence that a synthetic molecule has a particular form.  One approach to this is to try to match the experimental data about the symmetries of the molecule to the symmetries of a physical model of the desired form.  But molecules which are not completely rigid may have symmetries that are absent from the model.  In such a case, topology, which is the study of deformations of objects in space, can help  interpret the data. In this talk we will explore topological and geometric approaches to studying the symmetries of complex molecular structures.  No background in chemistry or mathematics is necessary.

Wednesday, April 4, 2018

Screening of “The Math Life”

Why did a magician become a mathematician? How can a person see in four dimensions? What does a mathematical proof have in common with a Picasso portrait? This elegant program brings to life the human dimension of mathematics through lively interviews with Freeman Dyson, David Mumford, Ingrid Daubechies, Persi Diaconis, Michael Freedman, Fan Chung Graham, Kate Okikiolu, Jennifer Tour Chayes, Peter Sarnak, Steven Strogatz, and seven other mathematicians. These captivating luminaries vividly communicate the excitement and wonder that fuel their work as they explore the world through its patterns, shapes, motions, and probabilities. Computer animations and analogies drawn from the visual arts are incorporated, to maximize accessibility to the fascinating concepts discussed. A Wendy Conquest/Bob Drake/Dan Rockmore Production. (51minutes)

Wednesday, February 28, 2018

Spring Mathematics and Statistics Department Tea

Join us for pizza and conversation! Bring your questions, meet faculty and learn about our major. Current majors and minors please come and share your experiences!

Wednesday, February 21, 2018

Speaker: Thomas Williemain, Ph.D., Industrial and Systems Engineering, Rensselaer Polytechnic Institute

Title:  Say Hello to Monte Carlo Simulation

Abstract: Monte Carlo simulation is a versatile methodology for analysis and design of stochastic systems. It is the go-to method when a problem is too complex for careful mathematical treatment.  This talk will introduce Monte Carlo methods by way ofexamples about inventory control for spare parts, ad-hoc communication networks, and/or bias in the sample standard deviation.

Thomas Willemain graduated from South Hadley High School, Princeton University and MIT. He has served on the faculties of MIT, Harvard, and RPI and has a parallel career as co-founder and Sr VP/Research at Smart Software, Inc. in Belmont, MA. He recently published a memoir, Working on the Dark Side of the Moon: Life Inside the National Security Agency.

He will linger after the talk to discuss graduate study in Industrial and Systems Engineering at RPI, software entrepreneurship, or other topics of interest.

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.