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 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)