BrainMap

Alexandru-Anton Popa

- INSTITUTUL DE MATEMATICA "SIMION STOILOW" AL ACADEMIEI ROMANE

Researcher

Curriculum Vitae (18/07/2023)

Expertise & keywords

Galois Representations and Modular Forms Call name: Projects for Young Research Teams - RUTE -2014 call
PN-II-RU-TE-2014-4-2077 2015 - 2017

Role in this project:

Coordinating institution: INSTITUTUL DE MATEMATICA "SIMION STOILOW" AL ACADEMIEI ROMANE

Project partners: INSTITUTUL DE MATEMATICA "SIMION STOILOW" AL ACADEMIEI ROMANE (RO)

Affiliation: INSTITUTUL DE MATEMATICA "SIMION STOILOW" AL ACADEMIEI ROMANE (RO)

Project website: http://www.galrepmodform.simplesite.com

Abstract:

The main preoccupations of this project belong to the field of Galois representations attached to modular forms. The project is divided in three main themes, each one of them has its own importance in the field and they represent three of the major directions in contributing to the scientific research:experimenting and formulating conjectures; finding the right (natural, canonical) tools and environments for certain problems; generalizing previous results.

The first direction is theoretical in its essence, but, as in our previous work, it will be accompanied by many explicit computations. This part tries to offer a unified view of some of recent results in the literature using P.I.’s and his collaborator previous work and is proposing a better understanding of the eigencurve and its classical points. The second part is experimental in its essence but is based on strong arguments and deep previous results by many important mathematicians. The experimental computations will create two databases attached to rational elliptic curves: one for the associated Galois representation modulo its conductor and the second one of the coefficients of the associated eigenform in terms of products of Eisenstein series. A study of interlinks between the two databases will be in our opinion of great importance. The third part is theoretical, but many practical experiments are needed. This part is aiming to obtain a generalization of previous results concerning congruences between modular forms

Randomness, Geometric Problems and Functional Inequalities Call name: Projects for Young Research Teams - TE-2011 call
PN-II-RU-TE-2011-3-0259 2011 - 2014

Role in this project:

Coordinating institution: Institutul de Matematica "Simion Stoilow" al Academiei Romane

Project partners: Institutul de Matematica "Simion Stoilow" al Academiei Romane (RO)

Affiliation:

Project website: https://dl.dropboxusercontent.com/u/30425445/PNII.html

Abstract:

The project proposed describes a series of problems from probability, geometry, functional analysis and number theory which revolves around randomness. One of the objects of importance is the Brownian motion (and couplings of it) which is tightly related to the geometry at hand, in particular gives or requires geometric-topological content about the underling space they live on.

Another face of randomness is that of large random matrices whose limit when the dimension goes to infinity is treated by free probability. In this limiting procedure, classical inequalities, as for example, transportation, Log-Sobolev and Poincare become their counterpart in free probability. Interestingly, these new objects have a life of their own which we want to unveil. Apart from the functional inequalities, the free probability can be used to describe the limiting distribution of matrices with dependencies.

The functional inequalities alluded above can be seen as instances of functional inequalities in infinite dimensions. In this line of ideas the project proposes to include analysis of functional inequalities associated to Wiener measure on path spaces on one hand and some associated to branching processes on the other.

In a different direction, the randomness appears also in number theory as distribution of certain sequences of numbers. Particularly interesting are the pair correlation of angles of hyperbolic lattices and Farey fractions in increasingly large balls.

Periods of modular forms Call name: EC-FP7
FP7-93352-248569 2019 -

Role in this project: Project coordinator

Coordinating institution: INSTITUTUL DE MATEMATICA AL ACADEMI EI ROMANE INSTITUTE OF MATHEMATICS SIMION STOILOW OF THE ROMANIAN ACA DEMY

Project partners: INSTITUTUL DE MATEMATICA AL ACADEMI EI ROMANE INSTITUTE OF MATHEMATICS SIMION STOILOW OF THE ROMANIAN ACA DEMY (RO)

Affiliation: INSTITUTUL DE MATEMATICA AL ACADEMI EI ROMANE INSTITUTE OF MATHEMATICS SIMION STOILOW OF THE ROMANIAN ACA DEMY (RO)

Project website:

Abstract:

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