The goal of the LSU Mathematics Student Colloquium is to give both undergraduate and graduate students the opportunity to hear and interact with speakers from across the country, providing information and perspective possibly relevant to their graduate and postgraduate careers.

Each invited speaker will spend several days at LSU, giving multiple talks and making himself or herself available to undergraduates.

Talks are not confined to the math department but open to everyone. Those majoring in related fields are encouraged to come.

We are a charted LSU student organization (constitution and bylaws). We are munificently funded by the Student Government Programming, Support, and Initiatives Fund (PSIF), and the LSU Mathematics Department. We are grateful for the generous past funding made by grants from the National Science Foundation (a VIGRE grant) and the Board of Regents.

Fall 2019

**Steven Leth**(November 18 - 19, 2019)

Steve’s research is mostly focused on applications of nonstandard methods to combinatorial number theory, an area that has been especially active in the last few years. Steve also has a long-standing interest in the teaching of mathematics at all grade levels, and is active in developing curriculum materials for pre-service teachers, as well as working with in-service teachers in a variety of professional development settings. Since receiving his doctoral degree from the University of Colorado in 1985, Steve spent three years as a “Van Vleck Assistant Professor” at the University of Wisconsin and is now in his 32^{nd} year at the University of Northern Colorado.

**Undergraduate Talk** ( Lockett 241; Monday, November 18, 1:30- 2:20 PM)

Title: Fixed Points of Continuous Functions in the plane

**Graduate Talk** ( Lockett 285 ; Tuesday, November 19, 1:30-2:20 PM)

**Keith Conrad**(October 31 - November 1, 2019)

Keith Conrad received his PhD at Harvard, and after postdoc positions at Ohio State, MSRI, and UC San Diego he moved to UConn. His research interests are in number theory, which he first learned about in high school as a student at the Ross program, and since then he has given talks on the subject to students at summer programs in the USA, China, and Russia.

**Graduate Talk** ( Coates 109; Thursday, October 31, 1:30- 2:30 PM)

Title: Heuristics for Statistics in Number Theory

**Undergraduate Talk** ( Allen 123 ; Friday, November 1, 9:30-10:20 AM)

**Peter Jorgensen**(April 12-22, 2019)

Professor Peter Jorgensen obtained his PhD from the University of Copenhagen in 1997. He held post doc positions in Antwerp, Bielefeld, and Copenhagen before moving to the University of Leeds in 2003 as a University Research Fellow. He has been Professor of Mathematics at Newcastle University since 2006. He is the author of more than 70 research papers and serves as a main editor of the Bulletin of the London Mathematical Society.

**Undergraduate Talk** ( Lockett 113 ; Friday, April 12, 10:30-11:20 AM)

Title: Knots

Abstract: Knots are everyday objects, but they are also studied in mathematics. They were originally envisaged as models for atoms by Lord Kelvin, and have been studied by increasingly sophisticated mathematical methods for more than 100 years.

Two knots are considered to be "the same" if one can be manipulated to give the other without breaking the string. The natural question of whether two given knots are the same turns out to be highly non-trivial; indeed, this is the central question of Knot Theory.

The talk is a walk through some aspects of this fascinating area of pure mathematics.

**Graduate Talk** ( Lockett 277; Monday, April 22, 3:30- 4:20 PM)

Title: Quiver representations and homological algebra

Fall 2018

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**Gilles Francfort**(April 3-5, 2019)

Dr. Francfort is a Professor of Mathematics at the Université Paris XIII and a visiting professor at the Courant Institute at New York University. He received his PhD in Mechanical Engineering at Stanford University and his habilitation at Université Paris 6. Dr. Francfort was a senior member of the Institut Universitaire de France in Paris, and a co-recipient of the Paul-Doistau-Emile Blutet prize from the French Academy of Sciences. He has traveled prolifically and has had many talks and invited stays at institutions throughout the world.

**Undergraduate Talk** ( Lockett 9; Wednesday, April 3, 3:30-4:20 PM)

Title: Spring Brake

Abstract: I wish to demonstrate that minimization is a natural notion when dealing with even simple mechanical systems. The talk will revolve mainly around a simple spring brake combination which will in turn illustrate how the search for minimizers tells us things are never as simple as first thought. All that will be needed for a correct understanding of the material are basic notions of convexity, continuity as well as some familiarity with integration by parts.

**Graduate Talk** ( Lockett 9; Friday, April 5, 3:30- 4:20 PM)

Title: The mysterious role of stability in defective solids

Fall 2018

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**Joseph Bonin**(November13-14, 2018)

Dr. Bonin has research interests in Matroid Theory, which is a branch of Combinatorics. He is a professor at The George Washington University, where he has been since receiving his PhD from Dartmouth College in 1989. He is a member of the GW Academy of Distinguised Teachers, and has been a research visitor at many universities, including MIT and Universitat Politecnica de Catalunya.

**Undergraduate Talk** ( Lockett 114; Tuesday, November 13, 3:30-4:20 PM)

Title: What do lattice paths have to do with matrices, and what is beyond both?

Abstract: A lattice path is a sequence of east and north steps, each of unit length, that describes a walk in the plane between points with integer coordinates. While such walks are geometric objects, there is a subtler geometry that we can associate with certain sets of lattice paths. Considering such sets of lattice paths will lead us to examine set systems and transversals, their matrix representations, and geometric configurations in which we put points freely in the faces of a simplex (e.g., a triangle or a tetrahedron). Matroid theory treats these and other abstract geometric configurations. We will use concrete examples from lattice paths to explore some basic ideas in matroid theory and some of the many intriguing problems in this field.

**Graduate Talk** ( Lockett 235; Wednesday, November 14, 1:30- 2:20 PM)

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**Joshua Sabloff**(October15-17, 2018)

Dr. Sabloff has research interests in Contact and Symplectic Geometry, especially Legendrian and Transversal Knot Theory. He received his PhD from Stanford University. After he spent a year as a postdoctoral lecturer at the University of Pennsylvania, he moved to Haverford. He is now an Associate Professor at Haverford College in Pennsylvania.

**Undergraduate Talk** ( 239 Lockett; Monday, October 15, 3:30-4:20 PM)

Title: How to Tie Your Unicycle in Knots: An Introduction to Legendrian Knot Theory

Abstract: You can describe the configuration of a unicycle on a sidewalk using three coordinates: two position coordinates x and y for where the wheel comes into contact with the ground and one angle coordinate t that describes the angle that the direction the wheel makes with the x axis. How are the instantaneous motions of the unicycle constrained (hint: do you want your tire to scrape sideways)? How can we describe that constraint using generalizations of tools from vector calculus?

The system of constraints at every point in (x,y,t)-space is an example of a "contact structure," and a path that obeys the constraints is a "Legendrian curve." If the curve returns to its starting point, then it is called a "Legendrian knot." A central question in the theory of Legendrian knots is: how can you tell two Legendrian knots apart? How many are there? In other words, how many ways are there to parallel park your unicycle?

There will NOT be a practical demonstration.

**Graduate Talk** ( 239 Lockett; Tuesday, October 16, 3:30- 4:20 PM)