Speaker:  Victor Vuletescu (University of Bucharest, Romania)

Title: Locally conformally Kahler metrics

Abstract:   Locally conformally Kahler metrics (LCK) were introduced by Izu Vaisman in the mid 70's as a substitute for
Kahler ones on manifolds which do not admit such metrics (e.g. Hopf surfaces). By the subsequent work of many people
in the next three decades, this kind of metrics were proven to exist on a large class of manifolds: for instance, "virtually all"
compact complex non-Kahler surfaces admit LCK metrics. The aim of this talk is to give a "state of the art" on the complex
structure of manifolds admitting LCK metrics, from the viewpoint of classification theory of (low-dimensional)  compact
complex manifolds. (Contact person: Rares Rasdeaconu)

Speaker:  Andrei Caldararu (University of Wisconsin, Madison)

Title: Yet another Moonshine

Abstract:  The j-function, introduced by Felix Klein in 1879, is an essential ingredient in the study of elliptic curves. It is
Z-periodic on the complex upper half-plane, so it admits a Fourier expansion. The original Monstrous Moonshine conjecture,
due to McKay and Conway/Norton in the 1980s, relates the Fourier coefficients of the j-function around the cusp to dimensions
of irreducible representations of the Monster simple group. It was proved by Borcherds in 1992. In my talk I will try to give
a rudimentary introduction to modular forms, explain Monstrous Moonshine, and discuss a new version of it obtained in joint
work with Yunfan He and Shengyuan Huang. Our version involves studying the j-function around CM points (so-called
Landau-Ginzburg points in the physics literature) and expanding with respect to a coordinate which arises naturally in string theory.

Speaker:  Manuel Rivera (Purdue University)

Title: An algebraic model for the free loop space

Abstract:   In this talk, I will describe a purely algebraic construction that models the passage from a topological space X to its free
loop space LX, the space of all continuous maps from the circle to X, based on an algebraic model for the underlying space X.
The construction has the advantage that it does not require any restrictions on the fundamental group, as other similar constructions
in the literature do.The construction to be discussed is a modified version of the coHochschild complex. The input is a coalgebra
over a ring equipped with additional structure and the output a chain complex with a "rotation" operator.  When this construction
is applied to the coalgebra of chains, suitably interpreted, of an arbitrary simplicial set S one obtains a chain complex quasi-isomorphic
to the chains on the free loop space of the geometric realization of S with its circle action. This algebraic construction is invariant
with respect to a notion of weak equivalence between coalgebras that enjoys enough homotopical flexibility to produce tractable models
for the free loop space of a non-simply connected space. (Contact Person: Anna Marie Bohmann)
            

Speaker: Ronan Conlon (University of Texas at Dallas)   

Title: Asymptotically conical Calabi-Yau manifolds

Abstract: Asymptotically conical Calabi-Yau manifolds are non-compact Ricci-flat Kahler manifolds that are modelled on a Ricci-flat
Kahler cone at infinity. I will present a classification result for such manifolds. This is joint work with Hans-Joachim Hein (Fordham/Muenster).
(Contact person: Rares Rasdeaconu)