Organizatori

• Prof. dr. Ioan Bucătaru
• Prof. dr. Cezar Oniciuc
• Prof. dr. Cătălin Galeş
• Prof. dr. Eugen Vărvărucă

Programul seminarului

Joi 11 decembrie, ora 16 (Sala de Conferinţe a Facultăţii de Matematică)

• Dr. Răzvan Teodorescu, University of South Florida, Extremal domains for analytic content in one complex dimension.

Abstract: For a compact K in the complex plane, the analytic content is defined as the (uniform) distance from the antiholomorphic variable to the set of rational functions with poles off K. For (closures of) domains with finite connectivity and rectifiable boundary, the analytic content is known to be bound from below by 2A/P, where A, P are the area and perimeter of the domain and its boundary, respectively. In this talk, I will present a solution to the problem (formulated in 1973) of finding the domains achieving this bound (extremal domains). This solution has surprisingly many interpretations: finding projective connections in the geometric Langlands program, finding Rankine vortices with arbitrary connectivty in fluid dynamics, or solving the chiral gauge problem in two dimensions for fiber group U(1), to name a few. Time permitting, other extensions of the problem will be discussed.

About the speaker: Razvan Teodorescu is a professor of mathematics at the University of South Florida. A graduate of Ecole Polytechnique (Maitrise 1995), "Al. I. Cuza" University (M.Sc. 1997) and University of Chicago (Ph.D. 2004), he works on mathematical physics problems at the intersection between complex geometry, representation theory, function theory, and non-commutative probability.

Vineri 9 mai 2025, ora 14 (Amfiteatrul Myller)

• Cezar Oniciuc, UAIC Iaşi, Despre o clasa de hipersuprafete biconservative in spatiul euclidian R^n.

Abstract: In aceasta expunere vom prezenta cateva rezultate obtinute anterior despre hipersuprafetele biconservative in spatiul euclidian R^n care sunt SO(p+1)×SO(q+1) invariante, n=p+q+2. Folosind rezultate din teoria Sistemelor Dinamice, vom studia comportamentul curbelor profil in spatiul orbitelor pentru aceste hipersuprafete aratand ca exista o clasa infinita de hipersuprafete biconservative, SO(p+1)×SO(q+1) invariante si complete.

Vineri 4 aprilie 2025, ora 15 (Amfiteatrul Myller)

• Razvan Liţcanu, UAIC Iaşi, Teorii de coomologie - exemple si principii generale II.

Abstract: Expunerea este consacrata unei introduceri in diverse teorii de coomologie, cu accentul pus pe cateva proprietati generale, conexiuni intre diverse teorii si posibila abordare axiomatica a unei teorii de coomologie. Va fi abordat punctul de vedere al topologiei algebrice si vor fi abordate teorii de coomologie pe spatii topologice.

Vineri 21 martie 2025, ora 14 (Amfiteatrul Myller)

• Razvan Liţcanu, UAIC Iaşi, Teorii de coomologie - exemple si principii generale I.

Abstract: Expunerea este consacrata unei introduceri in diverse teorii de coomologie, cu accentul pus pe cateva proprietati generale, conexiuni intre diverse teorii si posibila abordare axiomatica a unei teorii de coomologie. Va fi abordat punctul de vedere al topologiei algebrice si vor fi abordate teorii de coomologie pe spatii topologice.

Vineri 7 martie 2025, ora 14 (Amfiteatrul Myller)

• Marius Beceanu, Estimari de descrestere punctuala pentru ecuatii dispersive II.

Abstract: Voi prezenta rezultate noi si metode pentru demonstrarea descresterii punctuale a solutiilor ecuatiei lui Schroedinger si ecuatiei undelor. Voi incepe prin a prezenta aceste doua ecuatii si concepte importante legate de solutiile lor.

Marţi 25 februarie 2025, ora 18 (Sala de Conferinţe a Facultăţii de Matematică)

• Marius Beceanu, Estimari de descrestere punctuala pentru ecuatii dispersive I.

Abstract: Voi prezenta rezultate noi si metode pentru demonstrarea descresterii punctuale a solutiilor ecuatiei lui Schroedinger si ecuatiei undelor. Voi incepe prin a prezenta aceste doua ecuatii si concepte importante legate de solutiile lor.

Marţi 14 ianuarie 2025, ora 18 (Sala de Conferinţe a Facultăţii de Matematică)

• Răzvan-Dumitru Ceucă, Universitatea Tehnică Gheorghe Asachi Iaşi, Various results concerning homogenisation of nematic liquid crystals II.

Abstract: In this talk, we present first an introduction to nematic liquid crystals and then three results concerning homogenisation of nematic liquid crystals: two of them are in perforated domains, while the other one concerns rates of convergence for boundary homogenisation. The first work is a G-convergence result for the Landau-de Gennes model in 3D domains with connected perforations. The goal of the analysis is to find new terms in the energy functional that are independent of the gradient. The second result is an error estimate for a 2D toy model used to describe rugosity effects in nematic liquid crystals via homogenisation problems, using once again the Landau-de Gennes model. The last problem is a local L^2-convergence result for a homogenisation problem in two dimensions with isolated perforations. Here we use the Oseen-Frank model, with the goal of finding new gradient-dependent terms in the energy functional.

Marţi 17 decembrie 2024, ora 18 (Sala de Conferinţe a Facultăţii de Matematică)

• Răzvan-Dumitru Ceucă, Universitatea Tehnică Gheorghe Asachi Iaşi, Various results concerning homogenisation of nematic liquid crystals I.

Abstract: In this talk, we present first an introduction to nematic liquid crystals and then three results concerning homogenisation of nematic liquid crystals: two of them are in perforated domains, while the other one concerns rates of convergence for boundary homogenisation. The first work is a G-convergence result for the Landau-de Gennes model in 3D domains with connected perforations. The goal of the analysis is to find new terms in the energy functional that are independent of the gradient. The second result is an error estimate for a 2D toy model used to describe rugosity effects in nematic liquid crystals via homogenisation problems, using once again the Landau-de Gennes model. The last problem is a local L^2-convergence result for a homogenisation problem in two dimensions with isolated perforations. Here we use the Oseen-Frank model, with the goal of finding new gradient-dependent terms in the energy functional.

Marţi 3 decembrie 2024, ora 18 (Sala de Conferinţe a Facultăţii de Matematică)

• Cătălin Galeş, UAIC Iaşi, Dynamics modelling of space objects orbiting the Earth II.

Abstract: Since the launch of the Sputink 1 in 1957, a number of debris accumulated and now populates the circumterrestrial environment. These objects are found from Low Earth Orbits at altitudes of a few hundreds of kilometers to the Geostationary Earth Orbit, a region located at 42164 kilometers from the center of the Earth. The size of the debris runs from sub-millimeters to a few meters, but in view of their high velocities, they pose a serious threat for current and future satellites and are a source of hazard for human space spaceflights. The sustainability of future space activities is a priority for the current science and technology. In this context, it is important to make a thorough study of the dynamics of space debris, especially in view of determining regular and chaotic stability properties. In this work we illustrate the models that can describe the dynamics at different altitudes; such models strongly depend on the location of the debris, since at low altitudes one needs to consider the Earth's atmosphere, while lunisolar effects become more important at higher altitudes. After having introduced the equations of motion both in Cartesian and Hamiltonian formalism, we analyze the dynamics of different resonances, most notably the geosynchronous and semi-synchronous resonances. We also review some results about the study of the orbits in the LEO region.

Marţi 5 noiembrie 2024, ora 18 (Sala de Conferinţe a Facultăţii de Matematică)

• Cătălin Galeş, UAIC Iaşi, Dynamics modelling of space objects orbiting the Earth I.

Abstract: Since the launch of the Sputink 1 in 1957, a number of debris accumulated and now populates the circumterrestrial environment. These objects are found from Low Earth Orbits at altitudes of a few hundreds of kilometers to the Geostationary Earth Orbit, a region located at 42164 kilometers from the center of the Earth. The size of the debris runs from sub-millimeters to a few meters, but in view of their high velocities, they pose a serious threat for current and future satellites and are a source of hazard for human space spaceflights. The sustainability of future space activities is a priority for the current science and technology. In this context, it is important to make a thorough study of the dynamics of space debris, especially in view of determining regular and chaotic stability properties. In this work we illustrate the models that can describe the dynamics at different altitudes; such models strongly depend on the location of the debris, since at low altitudes one needs to consider the Earth's atmosphere, while lunisolar effects become more important at higher altitudes. After having introduced the equations of motion both in Cartesian and Hamiltonian formalism, we analyze the dynamics of different resonances, most notably the geosynchronous and semi-synchronous resonances. We also review some results about the study of the orbits in the LEO region.

Marţi 22 octombrie 2024, ora 18 (Sala de Conferinţe a Facultăţii de Matematică)

• Eugen Vărvărucă, UAIC Iaşi, Geometric approaches to water waves and free surface flows II.

Abstract: These lectures aim to present a new geometric approach to the asymptotic behaviour near singularities in some classical free-boundary problems in fluid dynamics. We start by introducing the problems and providing an outline of the methods that have been used to prove existence of solutions. We then present a modern proof, using monotonicity formulas and frequency formulas, of the famous Stokes conjecture from 1880, which asserts that at any stagnation point on the free surface of a two-dimensional steady irrotational gravity water wave, the wave profile necessarily has lateral tangents enclosing a symmetric angle of 120 degrees. (This result was first proved in the 1980s under restrictive assumptions and by somewhat ad-hoc methods.) We then explain how the methods extend to the case of two-dimensional steady gravity water waves with vorticity. Finally, we show how the same methods can be adapted to describe the asymptotic behaviour near singularities in the problem of steady three-dimensional axisymmetric free surface flows with gravity.

Marţi 8 octombrie 2024, ora 18 (Sala de Conferinţe a Facultăţii de Matematică)

• Eugen Vărvărucă, UAIC Iaşi, Geometric approaches to water waves and free surface flows I.

Abstract: These lectures aim to present a new geometric approach to the asymptotic behaviour near singularities in some classical free-boundary problems in fluid dynamics. We start by introducing the problems and providing an outline of the methods that have been used to prove existence of solutions. We then present a modern proof, using monotonicity formulas and frequency formulas, of the famous Stokes conjecture from 1880, which asserts that at any stagnation point on the free surface of a two-dimensional steady irrotational gravity water wave, the wave profile necessarily has lateral tangents enclosing a symmetric angle of 120 degrees. (This result was first proved in the 1980s under restrictive assumptions and by somewhat ad-hoc methods.) We then explain how the methods extend to the case of two-dimensional steady gravity water waves with vorticity. Finally, we show how the same methods can be adapted to describe the asymptotic behaviour near singularities in the problem of steady three-dimensional axisymmetric free surface flows with gravity.