# MSCS Seminar Calendar

Monday January 24, 2022

**Analysis and Applied Mathematics Seminar**

Packing and locomotion with friction

Silas Alben (U Michigan)

4:00 PM in Zoom

We discuss two problems dealing with the motions of thin deformable bodies under frictional forces. In the first problem, elastic filaments are confined within slowly-shrinking circular boundaries. The filaments undergo deformations that are a mixture of spiraling and bifurcations, primarily the former with small friction and the latter with large friction. With zero friction, a simple model predicts that the maximum curvature and the total elastic energy scale as the wall radius to the -3/2 and -2 powers respectively. With nonzero friction, the elastic energy follows a similar scaling but with a prefactor up to 8 times larger, due to delayering and bending with a range of small curvatures. The second problem examines models of snakes as thin filaments that deform and locomote due to friction. We examine optimal motions of two-link, three-link, and smooth bodies with a variety of friction coefficients. With large friction transverse to the snake, the optimal motion is a retrograde traveling wave with amplitude scaling as the friction coefficient the -1/4 power. With zero transverse friction, a triangular direct wave is optimal. Between these extremes we find a variety of local optima including standing waves (or ratcheting motions).

Wednesday January 26, 2022

**Commutative Algebra Seminar**

Partial Trace Ideals and Berger's Conjecture

Sarasij Maitra (University of Virginia)

3:00 PM in Zoom

We shall define an invariant that helps in obtaining information regarding the torsion submodule of a finitely generated rank one module over a one-dimensional Noetherian local domain. We shall briefly go through some properties of this and see how this can be applied to a long-standing conjecture of R. Berger concerning the module of differentials over an analytic $k$-algebra. If time permits, then we shall also state and prove an explicit computation of the invariant in this case.

Monday January 31, 2022

Monday February 7, 2022

Monday February 14, 2022

Monday February 21, 2022

Monday February 28, 2022

Wednesday March 2, 2022

Monday March 7, 2022

Wednesday March 9, 2022

Monday March 14, 2022

Wednesday March 30, 2022

Friday April 8, 2022

Wednesday April 13, 2022

Monday April 18, 2022

Wednesday April 20, 2022