Alternatively have a look at the program.

## What is higher Lie theory?

Lie theory" refers to a functorial correspondence between

finite-dimensional Lie algebras and 1-connected Lie groups, elucidated

by Sophus Lie and summarized in his three theorems, Lie I, II and III.

The first hint that there might be more to the story came from van Est

who noticed (and proved) that integrating higher Lie algebra cocycles

required higher connectivity assumptions on the Lie group. Furthermore,

attempts to build a Lie theory for Lie algebroids (and

infinite-dimensional Lie algebras) generally run into obstructions of a

## Generalized cohomology of M2/M5-branes

While it is well-known that the charges of F1/Dp-branes in type II string theory need to be refined from de Rham cohomology to certain twisted generalized differential cohomology theories, it is an open problem to determine the generalized cohomology theory for M2-brane/M5-branes in 11 dimensions. I discuss how a careful re-analysis of the old brane scan (arXiv:1308.5264 , arXiv:1506.07557, joint with Fiorenza and Sati) shows that rationally and unstably, the M2/M5 brane charge is in degree-4 cohomotopy.

## $L_\infty$ algebras governing simultaneous deformations in algebra and geometry

We will explain how simultaneous deformations problems in algebra and geometry are naturally governed by non quadratic $L_\infty$ algebras and how such algebras can be constructed by super geometry or operad theory, depending on the applications.

This will be illustrated with examples. We will consider simultaneous deformations of pairs such as couples of algebras/morphisms, coisotropic/Poisson, Dirac/Courant, generalized complex/Courant (if time permits).

## Open-closed homotopy algebras

Topological types of string worldsheets can be organised into a modular operad QP. For closed strings, algebras over this operad are essentially topological quantum field theories formalized by monoidal functors from cobordisms into vector spaces or by commutative Frobenius algebras. There is an analogous picture for open and open/closed strings. In the closed case, QP can be freely generated from certain cyclic suboperad P via modular envelope: in fact P=Com. In the open case, analogous result holds for P=Ass. In open-closed case, this problem is subtler.

## Rational homotopy of the little cubes operads and graph complexes

I will report on a joint work with Victor Turchin and Thomas Willwacher about the rational homotopy of the little cubes operads (equivalently, the little discs operads).

## Ginzburg--Kapranov criterion for Koszulness of operads, and its limitations

In their seminal paper on operadic Koszul duality, Ginzburg

and Kapranov established a remarkable functional equation that holds

whenever an operad is Koszul. I shall discuss some examples

demonstrating that non-Koszul operads do not have to violate that

criterion, in either of two possible ("weak" or "strong") senses.

## What good is a semi-model structure on algebras over an operad?

In general, it is difficult to transfer a model structure from a monoidal

model category M to the category of algebras over a (colored) operad P in M.

Often, one only ends up with a semi-model structure (i.e. where half the

factorization and lifting axioms only hold for maps with cofibrant domain),

and even this traditionally requires P to be Sigma-cofibrant. I?ll explain

what standard techniques still work in the context of semi-model categories,

so that users of model categories can get by if they only have a semi-model

## An Algebraic Combinatorial Approach to Opetopic Structure

The starting point of this talk will be an algebraic connection to be presented briefly between

the theory of abstract syntax of [1,2] and the approach to opetopic sets of [4]. This realization

conceptually allows us to transport viewpoints between these mathematical theories and I

will explore it here in the direction of higher-dimensional algebra leading to opetopic

categorical structures. The technical work will involve setting up a microcosm principle

for near-semirings and subsequently exploiting it in the cartesian closed bicategory of

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