# Seminars in geometry/topology

## Fall 2011

## Friday December 2, 10:15 - 12:00, room S21, Sentralbygg 2

Jacob Linder (Department of Physics):*Topological insulators*

**Abstract:** Topological insulators represent a very recently discovered quantum state of matter. In this talk, an introduction will be given to how topological order represents a new organizational principle of quantum matter in contrast to the usual paradigm of spontaneous symmetry breaking. We will show how quantum states of matter (including topological insulators) may be characterized by topological invariants, such as Chern numbers, which renders the quantum state robust toward perturbations and defects present in the material. Possible applications of topological insulators, including non-Abelian braiding statistics for use in quantum computation, will be briefly discussed.

## Thursday November 24, 13:15 - 15:00, room 738, Sentralbygg 2

Ole Chr. Lingjærde (University of Oslo): *Analysis on genomic data*

## (Proseminar) Monday November 7, 13:15 - 15:00, room S22, Sentralbygg 2

Marius Thaule:*Introduction to homotopy colimits*

**Abstract:** We will discuss three examples where we first compute the colimit and then compute the homotopy colimit. This talk is aimed at students.

## (Proseminar) Monday October 31, 13:15 - 15:00, room S22, Sentralbygg 2

Lars Sydnes:*Classical mechanics, connections and Riemannian geometry*

**Abstract:** The talk will explain how Riemannian geometry provides an excellent framework for discussing classical mechanics. The purpose is to provide an overview of elementary facts possibly useful to both topologists and geometers.

## Monday October 24, 13:15 - 15:00, room S22, Sentralbygg 2

Truls Bakkejord Ræder:*Knot theory and Khovanov homology*

**Abstract:** The talk will begin with a brief discussion of knot theory and knot
invariants. Having done this, I will give an introduction to the Khovanov
homology of knots. I will, in particular, give the construction of the
Khovanov chain groups and differential, and compute the homology of this
complex in a simple case.

## Monday October 17, 13:15 - 15:00, room S22, Sentralbygg 2

Magnus Bakke Botnan:*Zigzag persistence*

**Abstract:** Building on classical results from quiver theory we will develop a generalization of persistent homology called zigzag persistence. This theory addresses several interesting situations not previously covered. First the quiver theory will be used to justify the idea of zigzag persistence, but as existence proofs are not algorithmically favorable, we then roll up our sleeves and prove a theorem that allows us to develop an abstract algorithm.

## Monday October 10, 13:15 - 15:00, room S22, Sentralbygg 2

Gard Spreemann:*Introduction to topology and data*

**Abstract:** Measurement of an observable of a real-world system yields a discrete space of points. How does one investigate the underlying topology of the observable using these discrete samples? In this talk, I will give a brief introduction to one approach to the problem: persistent homology.

## Wednesday September 7, 13:15 - 15:00, room S21, Sentralbygg 2

Elke Markert (The Institute for Advanced Study):*Analysis of gene exprsseion data*

Markert is working in Levine's group at The Institute for Advanced Study in Princeton where they recently have made interesting progress in the expression analysis of major cancer types—in particular prostate cancer. She will report on their methods and findings.