(Joint work with Marco Golla and József Bodnár)
We will give a general overview of the plethora of concordance invariants which can be extracted from Ozsváth-Szabó-Rasmussen's knot Floer homology. 
We will then focus on the $\nu^+$ invariant and prove some of its useful properties. 
Furthermore we will show how it can be used to obstruct the existence of cobordisms between algebraic knots.

A cornerstone of the study of mapping class groups is the
Nielsen--Thurston classification theorem. I will outline a
polynomial-time algorithm that determines the Nielsen--Thurston type and
the canonical curve system of a mapping class. Time permitting, I shall
describe a polynomial-time algorithm to compute the quotient orbifold of
a periodic mapping class, and I shall discuss the conjugacy problem for
the mapping class group. This is joint work with Mark Bell.

Decorate knot cobordisms functorially induce maps on knot Floer homology.
We compute these maps for elementary cobordisms, and hence give a formula for 
the Alexander and Maslov grading shifts. We also show a non-vanishing result in the case of
concordances and present some applications to invertible concordances. 
This is joint work with Marco Marengon.
 

Configuration spaces of points in a manifold are well studied. Giving the points thickness has obvious physical meaning: the configuration space of non-overlapping particles is equivalent to the phase space, or energy landscape, of a hard spheres gas. But despite their intrinsic appeal, relatively little is known so far about the topology of such spaces. I will overview some recent work in this area, including a theorem with Yuliy Baryshnikov and Peter Bubenik that related the topology of these spaces to mechanically balanced, or jammed, configurations. I will also discuss work in progress with Robert MacPherson on hard disks in an infinite strip, where we understand the asymptotics of the Betti numbers as the number of disks tends to infinity. In the end, we see a kind of topological analogue of a liquid-gas phase transition.

We characterize cutting arcs on ber surfaces that produce new ber surfaces,
and the changes in monodromy resulting from such cuts. As a corollary, we
characterize band surgeries between bered links and introduce an operation called
generalized Hopf banding. We further characterize generalized crossing changes between
bered links, and the resulting changes in monodromy.

This is joint work with Matt Rathbun, Kai Ishihara and Koya Shimokawa

The mathematical design of the table flood demonstrator Wetropolis will be presented. Wetropolis illustrates the concepts of extreme rainfall and flooding.

It shows how extreme rainfall events  can cause flooding of a city due to groundwater and river flood peaks. Rainfall is supplied randomly in space using four outcomes (in a reservoir, on a moor, at both places or nowhere) and randomly in time using four rainfall intensities (1s, 2s, 4s, or 9s during a 10s Wetropolis day), including one extreme event, via two skew-symmetric discrete probability distributions visualised by two Galton boards. Wetropolis can be used for both public outreach and as scientific testing environment for flood mitigation and data assimilation.

More information: https://www.facebook.com/resurging.flows

The spreading of a viscous fluid in between a rigid, horizontal substrate and an overlying elastic sheet is presented as a simplified model of the hydraulic fracturing process. In particular, the talk will focus on the case of a permeable substrate for which leak-off arrests the propagation of the fluid and permits the development of a steady state. The different regimes of  gravitationally-driven and elastically-driven flow will be explored, as will the cases of a stiff and flexible sheet, before a discussion of the influence that particles included in the fluid have on the fracture propagation. 

 In this introduction for topologists, we explain the role that extensions of L-infinity algebras by taking homotopy fibers plays in physics. This first appeared with the work of physicists D'Auria and Fre in 1982, but is beautifully captured by the "brane bouquet" of Fiorenza, Sati and Schreiber which shows how physical objects such as "strings", "D-branes" and "M-branes" can be classified by taking successive homotopy fibers of an especially simple L-infinity algebra called the "supertranslation algebra". We then conclude by describing our joint work with Schreiber where we build the brane bouquet out of the homotopy theory of an even simpler L-infinity algebra called the superpoint.

 
The dimension of a finite-dimensional vector space V can be computed as the trace of the identity endomorphism id_V.  This dimension is also the value F_V(S^1) of the circle in the 1-dimensional field theory F_V associated to the vector space.  The trace of any endomorphism f:V-->V can be interpreted as the value of that field theory on a circle with a defect point labeled by the endomorphism f.  This last invariant makes sense even when the vector space is infinite-dimensional, and gives the trace of a trace-class operator on Hilbert space.  We introduce a 2-dimensional analog of this invariant, the `2-trace'.  The 2-dimension of a finite-dimensional separable k-algebra A is the dimension of the center of the algebra.  This 2-dimension is also the value F_A(S^1 x S^1) of the torus in the 2-dimensional field theory F_A associated to the algebra. Given a 2-endomorphism p of the algebra (that is an element of the center), the 2-trace of p is the value of the field theory on a torus with a defect point labeled by p.  Generalizations of this invariant to other defect configurations make sense even when the algebra is not finite-dimensional or separable, and this leads to a general notion of 2-trace class and 2-trace in any 2-category.  This is joint work with Andre Henriques.