"The heavy quark form factors are among the most important ingredients in top quark physics. In the first part of this talk, we present the computational method to obtain the three loop QCD corrections to the heavy quark form factors. We use a novel technique based on differential equations, to obtain the master integrals. In the second part of the talk, we study the high energy behaviour of these form factors. We present the corresponding renormalization group equation which not only governs the structure of infrared divergences, but also controls the Sudakov logarithms."

"Let $\mathfrak{gl}(n)$ denote the Lie algebra of the general linear group $GL(n). Given two finite dimensional irreducible representations $L(\lambda), L(\mu)$ of $\mathfrak{gl}(n)$, its tensor product decomposition $L(\lambda) \otimes L(\mu)$ is given by the Littlewood-Richardson rule. The situation becomes much more complicated when one replaces $\mathfrak{gl}(n)$ by the general linear Lie superalgebra $\mathfrak{gl}(m|n)$. The analogous decomposition $L(\lambda) \otimes L(\mu)$ is largely unknown. Indeed many aspects of the representation theory of $\mathfrak{gl}(m|n)$ are more akin to the study of Lie algebras and their representations in prime characteristic or to the BGG category $\mathcal{O}$. I will give a survey talk about this problem and explain why some approaches don't work and what can be done about it. This will give me the chance to speak about a) the character formula for an irreducible representation $L(\lambda)$, b) Deligne's interpolating category $Rep(GL_t)$ for $t \in \mathbb{C}$ and c) the process of semisimplification of a tensor category."

"A zero cycle on a k-variety X is any element of the free abelian group of closed points of X and its degree is the sum of its coefficients, weighted by the degrees of the residue fields of the closed points involved. Any k-rational point of X is a zero cycle of degree one. In this talk, we discuss Serre’s injectivity question which asks whether the converse is true for principal homogeneous spaces X/k under connected linear algebraic groups G/k, i.e. whether such an X admitting a zero cycle of degree one in fact has a rational point.  This naturally brings into the picture the so-called norm principles, which examine the behaviour of the images of group morphisms over field extensions from a linear algebraic group into a commutative one with respect to the norm map. Norm principles are interesting in their own right and have been previously studied by Merkurjev-Gille, especially in conjunction to the rationality of the algebraic group in question. However a result of Merkurjev and Barquero shows that the norm principle holds for all classical reductive groups of type A,B,C without any rationality assumptions with type D still remaining open. If time permits, we will report progress on the type D case (which part is joint work with Chernousov and Merkurjev)."

"I will introduce some recent work [1, 2] on formulating contextuality within the Spekkens framework [3] for scenarios that are traditionally considered in Kochen-Specker (KS) contextuality [4, 5]. I will follow Ref. [1] in motivating the discussion and then present a hypergraph framework that applies to KS-colourable contextuality scenarios, obtaining noise-robust noncontextuality inequalities that generalize the KS-noncontextuality bounds from Ref. [4]. The framework for Ref. [1] relies on the introduction of a new hypergraph invariant in obtaining the noncontextuality inequalities. We will see that this hypergraph invariant is, in fact, the only relevant invariant when it comes to obtaining noncontextuality inequalities for KS-uncolourable scenarios and we will outline a complementary framework for the latter following Ref. [2]. Taken together, Refs. [1, 2] complete the project of turning proofs of Kochen-Specker theorem – whether statistical or logical – into noise-robust noncontextuality inequalities following the Spekkens framework. Along the way, time permitting, we will also comment on the status of Specker’s principle [6] in these considerations and outline applications of the framework to quantum information protocols. References [1] R. Kunjwal, “Beyond the Cabello-Severini-Winter framework: Making sense of contextuality without sharpness of measurements”, arXiv:1709.01098 [quant-ph] (2018). [2] R. Kunjwal, “Hypergraph framework for irreducible noncontextuality inequalities from logical proofs of the Kochen-Specker theorem”, arXiv:1805.02083 [quant-ph] (2018). [3] R. W. Spekkens, “Contextuality for preparations, transformations, and unsharp measurements”, Phys. Rev. A 71, 052108 (2005). [4] A. Cabello, S. Severini, and A. Winter, “Graph-Theoretic Approach to Quantum Correlations”, Phys. Rev. Lett. 112, 040401 (2014). [5] A. Acín, T. Fritz, A. Leverrier, and A. B. Sainz, A Combinatorial Approach to Nonlocality and Contextuality, Comm. Math. Phys. 334(2), 533-628 (2015). [6] A. Cabello, “Specker ’s fundamental principle of quantum mechanics”, arXiv:1212.1756 [quant-ph] (2012)."