18 JAN 2021
11:00 - 12:00

Based on
https://www.sciencedirect.com/science/article/abs/pii/S016890022030961X


Abstract: Nowadays, several thousand accelerators are at work around the world in an extensive area of applications, ranging from industrial processes to scientific discoveries. Indeed, today’s particle accelerators not only address many of the confronting challenges like energy, economy and industry for the worldwide nations, but also serve as a unique tool to probe/search new physics that govern the universe. In this way, the next generation of colliders and in particular CERN, specifically in the AWAKE project, play the most important role for the current and ongoing challenges in high-energy physics experiments.

In this talk, we will have a brief introduction to the AWAKE experiment and specially our contribution alongside where we are designing a new photo-injector with very critical parameters. In this way, first through a detailed beam dynamic study we investigate on time evolution of envelopes and emittance of bunched beams in photo-injectors which in turns leads to a new model for describing the bunch behavior in the electron sources. Finally, we apply our model for the design of an ultra-short bunch photo-injector of the AWAKE experiment and present the simulation results.


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

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

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

27 JAN 2021
16:00 - 17:30

Organized by: School of Cognitive Sciences
to receive the link to join online, please send email to theoretical.neurosci.ipm@gmail.com

Abstract:


To unravel the functional properties of the brain, we need to untangle how neurons interact with each other and coordinate in large-scale recurrent networks. One way to address this question is to measure the functional influence of individual neurons on each other by perturbing them in vivo. Application of such single-neuron perturbations in mouse visual cortex has recently revealed feature-specific suppression between excitatory neurons, despite the presence of highly specific excitatory connectivity, which was deemed to underlie feature-specific amplification. Here, we studied which connectivity profiles are consistent with these seemingly contradictory observations, by modeling the effect of single-neuron perturbations in large-scale neuronal networks. Our numerical simulations and mathematical analysis revealed that, contrary to the prima facie assumption, neither inhibition dominance nor broad inhibition alone were sufficient to explain the experimental findings; instead, strong and functionally specific excitatory-inhibitory connectivity was necessary, consistent with recent findings in the primary visual cortex of rodents. Such networks had a higher capacity to encode and decode natural images, and this was accompanied by the emergence of response gain nonlinearities at the population level. Our study provides a general computational framework to investigate how single-neuron perturbations are linked to cortical connectivity and sensory coding and pave the road to map the perturbome of neuronal networks in future studies.


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