The copepod model is a simplification of the 3-link Purcell swimmer and is relevant to analyze more complex micro-swimmers. The mathematical model is validated by observations performed by a team from Hawaii, showing the agreement between the predicted and observed motions. Sub-Riemannian geometry will be introduced, assuming that displacements are minimizing the expanded mechanical energy of the micro-swimmer. The objective is to maximize the efficiency of a stroke (the ratio between the displacement produced by a stroke and its length). Using the Maximum Principle in the framework of Sub-Riemannian geometry, this leads to analyze family of periodic controls producing strokes to determine the most efficient one. Finally a robotic copepod is presented whose aim is to validate the computations and very preliminary results are given.

Sub-Riemannian geometry, Hamiltonian dynamics, Micro-swimmers, Copepod nauplii and Copepod robot Sponsored by the Meyer Fund

Tue, Mar. 17 11am (MATH 350)

Number Theory

Cliff Blakestad (Pohang University of Science and Technology) TBA

CANCELED Tue, Mar. 17

Kempner

Uri Shapira (Israel Institute of Technology)

X

Given an integral vector, there are several geometric and arithmetic objects one can attach to it. For example, its direction (as a point on the unit sphere), the lattice obtained by projecting the integers to the othonormal hyperplane to the vector, and the vector of residues modulo a prime p to name a few. In this talk I will discuss results pertaining to the statistical properties of these objects as we let the integral vector vary in natural ways.

Geometry of integral vectors

CANCELED Tue, Mar. 17

Grad Algebra Seminar

Nik Ruskuc (St Andrews, UK) The number of countable subdirect powers of a finite semigroup Sponsored by the Meyer Fund

Klaus Hulek (Institute for Algebraic Geometry, Leibniz University Hannover)

X

Bogomolov, Petrov and Tschinkel defined monodromy strata in the moduli space of elliptic K3 surfaces (BPT strata) and they also proved that these strata are rational. Here we compare (some of) these BPT strata to moduli spaces of lattice polarized K3 surfaces. More precisely, we classify all moduli spaces of lattice polarized K3 surfaces which dominate finite to one one of the BPT strata. This is closely related to Shimada's classification of connected components of the moduli of elliptic K3 surfaces. This is joint work with Michael L\“onne.

Elliptic K3 surfaces - monodromy strata versus lattice polarizations Sponsored by the Meyer Fund