26 JAN 2021
18:30 - 20:30

Abstract: The identification of attractor behavior offers some hope for a conceptually straightforward albeit simplified picture of quark-gluon plasma physics following a relativistic heavy-ion collision. The strong longitudinal expansion which characterizes the dynamics - at least in some model systems - leads to attractor behavior already at very early times. This expansion-driven universality makes it possible to connect features of the system at asymptotically small times to observables that reflect late time physics. I will review some of these developments, including recent work aiming at exploring features of early-times. I will also describe recent attempts to reformulate this circle of ideas in a way that would offer hope of going beyond the boost-invariance assumption which underlies the aforementioned studies.


https://us02web.zoom.us/j/84943560023?pwd=MGYzSmk4SlhoRTlxUEVhK01RMGxMZz09

25 JAN 2021
11:00 - 12:00

Based on
https://link.springer.com/article/10.1007%2FJHEP06%282018%29001


Abstract: A search for lepton flavour violating decays of the Higgs boson in the $\mu \tau$ and $e\tau$ decay modes is presented. The search is based on a data set corresponding to an integrated luminosity of $35.9 fb^{-1}$ of proton-proton collisions collected with the CMS detector in 2016, at a centre-of-mass energy of 13 TeV. No significant excess over the standard model expectation is observed.


https://meet.google.com/cph-xgtg-wfw

21 JAN 2021
11:00 - 13:00

Shortly after Eckmann and Schopf's definition of the concept of an injective modules, Matlis showed that the injective hull of a simple module over a commutative Noetherian ring R is Artinian. Vamos showed that the latter condition is actually equivalent to the commutative ring R being locally Noetherian. However, injective hulls of simple modules over non-commutative Noetherian rings might not be Artinian. Slightly different, but related, one might consider Noetherian algebras A over a field F and ask whether any finitely generated submodule of the injective hull of a finite dimensional simple A-module need to be finite dimensional. In other words, is the category of locally finite dimensional representations of A closed under taking injective hulls. This is certainly the case for commutative algebras, but not for non-commutative algebras. Feldvoss proved, using results of Donkin and Dahlberg, that the category of locally finite dimensional representations over an enveloping algebra $U(g)$ of a finite dimensional Lie algebra $g$ is closed under taking injective hulls if and only if $g$ is a solvable Lie algebra. Furthermore, the group ring $F[G]$ of a polycyclic-by-finite group also has this property. Having these motivating examples in mind we intend to find necessary and sufficient conditions for the category of locally finite dimensional representations over a Noetherian algebra A over a field F to be closed under taking injective hulls.

In the first talk we will characterize Noetherian algebras A whose category of locally finite dimensional representations is essentially closed through their finite dual coalgebra
$$A^circ = {f in Hom(A,F): mathrm{Ker}(f) mbox{ contains an ideal of finite codimension}}$$ and provide sufficient conditions that involve the maximal ideals of A of finite codimension. We then consider Ore extensions of an algebra A, which are non-commutative polynomial rings in a variable x such that the coefficients in A obey to $$xa = sigma(a)x+delta(a) , qquad forall a in A$$ for a given automorphism $sigma$ and a $sigma$-derivation $delta$ of $A$. As an important tool we will use the Rees ring of an ideal in the Ore extension and find condition under which it is Noetherian.

In the second talk we will provide some background on the theory of Hopf algebras, having in mind that enveloping algebras of Lie algebras and group algebras are fundamental example. We will show that the question of the category of locally finite dimensional representations of a Noetherian Hopf algebra to be essentially closed can be reduced to the study of finitely generated extensions of the trivial representation. Our main results will show that Ore extension of commutative Noetherian Hopf algebras, certain Hopf crossed product algebra $A#_sigma H$ and all affine Hopf algebra domains of Gelfand-Kirillov dimension $leq 2$ with $Ext_H^1(F,F)
eq 0$ are Noetherian algebras whose category of locally finite representations is essentially closed.

Throughout the talks we will assume that the base field is algebraically closed and has characteristic zero.

The talks will be based on the preprint ``Locally Finite Representations Over Noetherian Hopf algebras" jointly written with my coauthor Can Hatipoglu. A PDF of this preprint can be found on ArXiv: href{https://arxiv.org/abs/2010.14192}{ exttt{https://arxiv.org/abs/2010.14192}}





Access link:


https://meet.google.com/ndk-abim-gxy

21 JAN 2021
11:00 - 12:00

Journal Club
http://meet.google.com/iys-ixfq-gwm

20 JAN 2021
16:30 - 18:00

The ancient Greek word "geometry" is, with its etymological meaning of "measurement of the earth", one of the oldest of mathematics. The discovery of non-euclidean geometries in the 19th century dramatically increased the scope of geometry. This scope was further extended in the 20th century by dividing geometry into branches differing in their objects of study and their methods: topology, differential geometry, Riemannian geometry, symplectic geometry, complex geometry, algebraic geometry, ... Grothendieck is known primarily for having re-founded algebraic geometry on entirely new bases. But he himself considered himself to be a general mathematician, not a specialist. So one may wonder whether the word "geometry", which he used very often without ever defining it, has for him a precise meaning that goes beyond algebraic geometry, and whether certain notions he introduced or to which he gave a central role are likely to apply to everything that one might imagine to be called geometric. The aim of the presentation will be to propose elements of an answer to this question.

To get more information about the colloquium, join to the following google group:
https://groups.google.com/g/ipm-math-colloquium

20 JAN 2021
11:00 - 12:00

Abstract: We propose a mass-dependent MOM scheme to renormalize UV divergence of unpolarized PDFs at one-loop order. This approach which is based on a once subtracted dispersion relation does not need any regulator. The overall counterterms are obtained from the imaginary part of large transverse momentum region in loop integrals.
The mass-dependent characteristic of the scheme yields to mass-dependent splitting functions for the DGLAP evolution equations. While the flavor number is fixed at any renormalization scale, the decoupling theorem is automatically imposed by the mass-dependent splitting functions. The required symmetries are also automatically respected by our prescription.


https://meet.google.com/dmk-zowd-cmo


Indico: https://indico.particles.ipm.ir/indico/event/398

20 JAN 2021
13:30 - 15:00

The equilibrium state of fields in the causal wedge of a dS observer is thermal, though realistic observers have only partial access to the state. To them, out-of-equilibrium states of a light scalar field appear to thermalize in a Markovian fashion. We show this by formulating a systematic expansion for tracing out the environment. As an example, we calculate the O(\lambda) correction to the result of Starobinsky and Yokoyama for the relaxation exponents of $\lambda\phi^4$ theory.