## GEOTOP-A SEMINAR SERIES

**Speaker:**De Witt L. Sumners

**Title:**DNA Topology

**Keywords:**DNA, topoisomerase, site-specific recombination, knots, links, tangle model, supercoiling, viral capsids

**Date:**August 17, 2018

Cellular DNA is a long, thread-like molecule with remarkably complex topology. Enzymes that manipulate the geometry
and topology of cellular DNA perform many vital cellular processes (including segregation of daughter chromosomes, gene
regulation, DNA repair, and generation of antibody diversity). Some enzymes pass DNA through itself via enzyme-bridged
transient breaks in the DNA; other enzymes break the DNA apart and reconnect it to different ends. In the topological
approach to enzymology, circular DNA is incubated with an enzyme, producing an enzyme signature in the form of DNA knots
and links. By observing the changes in DNA geometry (supercoiling) and topology (knotting and linking) due to enzyme action,
the enzyme binding and mechanism can often be characterized. This talk will discuss topological models for DNA strand passage
and exchange, including the analysis of site-specific recombination experiments on circular DNA and the analysis of packing
geometry of DNA in viral capsids.

**Speaker:**Rafael Herrera

**Title:**A brief introduction to Discrete Exterior Calculus

**Keywords:**differential forms, Hodge star operator, simplicial complex, boundary operator

**Date:**September 7, 2018

Discrete Exterior Calculus (DEC) is a relatively new method for solving partial differential equations
numerically. The central idea of the method is to develop a discrete version of Exterior Differential
Calculus. In this talk, we will briefly review the various operators of Exterior Differential Calculus
and their discrete versions. We will then focus our attention in 2D DEC, presenting a geometric
interpretation of DEC as well as numerical comparisons with the Finite Element Method in order to show
DECâ€™s competitive performance.

**Speaker:**Cristian Micheletti

**Title:**Knotted DNA: conformational, dynamical and pore-translocation properties

**Keywords:**pore translocation, DNA knots, DNA supercoiling

**Date:**September 21, 2018

Knots and supercoiling are both introduced in bacterial plasmids by catalytic processes involving
DNA strand passages. I will report on a recent study where we used molecular dynamics simulations and a mesoscopic
DNA model, to study the simultaneous presence of knots and supercoiling in DNA rings and the kinetic and metric
implications which may be relevant for the simplyfing action of topoisomerases. Finally, I will discuss how the same
modelling and simulation approach can be used shed light on the complex experimental phenomenology of knotted DNA
translocating through solid state nanopores.

**Speaker:**Vidit Nanda

**Title:**Discrete Morse Theory

**Keywords:**discrete Morse theory, persistent homology, cellular sheaf theory, flow category

**Date:**October 19, 2018

Large-scale homology computations are rendered tractable in practice by
a combinatorial version of Morse theory. Assuming that my internet connection survives, in
this talk I will introduce discrete Morse theory, describe how it helps with computing
various types of homology, and outline a powerful new higher-categorical extension. The
audience will not require prior knowledge of any of the technical terms mentioned above.

**Speaker:**Jesus Gonzalez

**Title:**Simplicial complexity: piecewise linear motion planning in robotics.

**Keywords:**topological complexity, simplicial topology, simplicial aproximation, contiguity of maps

**Date:**November 9, 2018

Using the notion of contiguity of simplicial maps, and its relation (via iterated
subdivisions) to the notion of homotopy between continuous maps, we adapt Farber's topological complexity
to the realm of simplicial complexes. We show that, for a finite simplicial complex K, our discretized
concept recovers the topological complexity of the realization of K.