Geometry seminar at IMAR

Spring 2025

Date / Time	Speaker	Title	Location
April 24, 2025 11:15	Mihajlo Cekic Creteil	Semiclassical methods in dynamics and geometry	IMAR room 307
April 24, 2025 10:00	Nicolina Istrati Angers	On some properties of Hopf manifolds	IMAR room 307
April 23, 2025 11:15	Louis Beaufort Orsay	How (not) to geometrize dynamics	IMAR room 307
April 23, 2025 10:00	Raluca Tanase IMAR	Geometric methods in complex dynamics	IMAR room 307
April 15, 2025 11:15	Andrei Moroianu IMAR & Orsay	Gauduchon metrics in conformal geometry	IMAR room 307
April 15, 2025 10:00	Vlad Marchidanu IMAR	An Aubin-Yau Theorem for Transversally Kahler Foliations	IMAR room 307
April 14, 2025 11:15	Sergiu Moroianu IMAR	Asymptotics of the Selberg Zeta function on the Teichmuller space	IMAR room 307
April 14, 2025 10:00	Cezar Joita IMAR	The ED discriminant for plane curves	IMAR room 307
April 11, 2025 11:15	David Petcu Universitatea Bucuresti	Automorphisms of Inoue surfaces S^+	IMAR room 307
April 11, 2025 10:00	Jose Luis Carmona-Jimenez IMAR	The Ambrose-Singer Theorem for cohomogeneity one manifolds	IMAR room 307
April 10, 2025 11:15	Miron Stanciu IMAR	Special non-Kahler metrics on solv and nilmanifolds	IMAR room 307
April 10, 2025 10:00	Victor Vuletescu Universitatea Bucuresti	On LCK threefolds with algebraic dimension one	IMAR room 307
April 8, 2025 11:15	Adrien Boulanger Marsilia	Linking invariant measures of a vector field	IMAR room 307
April 8, 2025 10:00	Dragos Manea IMAR	Discrete Laplacians on the hyperbolic space - a compared study	IMAR room 307
April 3, 2025 11:15	Mihaela Pilca Regensburg	Conformal product structures on compact Kahler manifolds	IMAR room 307
April 3, 2025 10:00	Liviu Ornea IMAR	Special non-Kahler metrics	IMAR room 307
April 2, 2025 14:00	Florin Belgun IMAR	Structure of curves in conformal manifolds	IMAR room 307
April 1, 2025 11:00	Nefton Paly Orsay	On maximal totally real embeddings	IMAR room 307
March 25, 2025 10:00	Mihaela Pilca Regensburg	Einstein metrics on conformal products	IMAR room 307
Abstract: I will speak about conformal product structures which contain an Einstein metric. More precisely, we will see that, under some natural geometric assumption, Einstein metrics on conformal products of two compact conformal manifolds are warped product metrics. This talk is based on joint work with Andrei Moroianu.
March 18, 2025 10:00	Carlos Shahbazi UNED Madrid	Heterotic geometry and locally conformally Kahler surfaces	IMAR room 307
Abstract: In 2005, S.-T. Yau proposed the Hull-Strominger system as the natural generalization of the Calabi problem to non-Kahler complex geometry. The Hull-Strominger system is a gauge differential system that occurs as the supersymmetry conditions of Heterotic supergravity and that has become a fundamental tool in the study of the moduli space of Calabi-Yau three-folds. In this talk, I will provide a pedagogical introduction to the geometry of Heterotic supergravity with the end goal of proposing an extension of the Hull-Strominger system that is naturally adapted to the study of locally conformally Kahler complex surfaces.
March 4, 2025 10:00	Gheorghe Craciun Wisconsin	Polynomial dynamical systems and reaction networks: a geometric approach for proving the global attractor conjecture	IMAR room 307
Abstract: The mathematical analysis of global properties of polynomial dynamical systems can be very challenging (for example: the second part of Hilbert's 16th problem, or the analysis of chaotic dynamics in the Lorenz system). On the other hand, any dynamical system with polynomial right-hand side can essentially be regarded as a model of a reaction network. Key properties of reaction networks are closely related to fundamental results about global stability in classical thermodynamics. For example, the Global Attractor Conjecture can be regarded as a finite dimensional version of Boltzmann's H-theorem. We will discuss some of these connections, as well as the introduction of toric differential inclusions as a tool for proving the Global Attractor Conjecture. We will especially focus on the geometric structure of toric differential inclusions, and on the geometric characterization of their invariant regions. This presentation will be completely self-contained, and will be accessible to students. In particular, no previous knowledge will be assumed about polynomial dynamical systems, differential inclusions, reaction networks, or thermodynamics.
February 25, 2025 10:00	Costin Vilcu IMAR	Skeletal Cut Loci on Convex Polyhedra	IMAR room 307
Abstract: The talk is based on the joint work 2312.01534 with J. O'Rourke. We study skeletal cut loci on convex polyhedra (i.e., cut loci included in the 1-skeleton of the respective polyhedron), obtaining four main results. First, given any combinatorial tree T, there exists a convex polyhedron and a point with a skeletal cut locus that matches the combinatorics of T. Second, any (non-degenerate) polyhedron has at most a finite number of points with skeletal cut loci. Third, we show that almost all polyhedra have no skeletal cut locus. Fourth, we provide a combinatorial restriction to the existence of skeletal cut loci.
February 18, 2025 10:00	Liana David IMAR	Teorema lui Darboux pentru structuri complexe generalizate pe algebroizi Courant tranzitivi	IMAR room 307
Abstract: Voi studia forma locala a structurilor complexe generalizate pe algebroizi Courant tranzitivi. Rezultatul principal al expunerii va include ca si cazuri extreme teorema lui Darboux-Gualtieri despre structuri complexe generalizate pe varietati, si, de asemenea, descrierea lui Wang a structurilor complexe stang invariante pe grupuri Lie compacte, semisimple. Lucrare in colaborare cu Vicente Cortes.
January 21, 2025 10:00	Florin Belgun IMAR	Structuri proiective pe curbe: de la geometrie conforma la ecuatia Hill	IMAR room 307
Abstract: Pe orice curba intr-o varietate confoma de dimensiune cel putin 3 exista un operator liniar de ordinul 2 canonic definit. In orice parametrizare acest operator induce o ecuatie liniara de ordinul 2 de tipul Hill: x''+Fx=0, cu F o functie. Aceasta functie este zero pentru parametrizarile locale proiective, care astfel induc o structura proiectiva pe curba. Acestea pot fi clasificate in functie de clasele de conjugare in acoperirea universala a lui SL(2,R) dar ecuatiile Hill nu pot fi rezolvate explicit in general. Avem cateva criterii pentru a estima tipul de structura proiectiva.

Fall 2024

Date / Time	Speaker	Title	Location
December 10, 2024 10:00	Gabriel Baditoiu IMAR	Lax pair equations and Connes-Kreimer renormalization	IMAR room 307
Abstract: I review the Lax pair equations introduced in my paper with Steven Rosenberg (CMP 296 (2010), 655--680) and several examples of compelely integrable Lax pair equations for certain low-dimensional Lie algebras of infinitesimal characters (https://arxiv.org/abs/2312.00901 )
November 12, 2024 10:00	David Petcu Universitatea Bucuresti	Ambrose-Singer theorems III	IMAR room 307
Abstract: We begin with a brief introduction on the structure of automorphism groups of non-Kahler compact surfaces. We then compute the group for the Inoue surfaces of type S+/S- by using their respective associated number fields.
October 15, 2024 10:00	Jose Luis Carmona-Jimenez IMAR	Ambrose-Singer theorems III	IMAR room 307
Abstract: The Tricerri-Vanhecke's Program for Symplectic Geometry: We present the Ambrose-Singer Theorem for general homogeneous manifolds and apply the Tricerri-Vanhecke program to symplectic and Fedosov manifolds.
October 8, 2024 10:00	Jose Luis Carmona-Jimenez IMAR	Ambrose-Singer theorems II	IMAR room 307
Abstract: The Homogeneous Geometries of the Complex Hyperbolic Space: A homogeneous geometry of the complex hyperbolic space is understood as a transitive action by isometries on it, together with an Ambrose-Singer connection. Surprisingly, comprehensive lists of all homogeneous descriptions of such spaces are unknown in many cases. We compute all the Ambrose-Singer connections in the complex hyperbolic space, its homogeneous structures, and classify them in terms of the holonomy of the Ambrose-Singer connection.
October 1, 2024 10:00	Jose Luis Carmona-Jimenez IMAR	Ambrose-Singer theorems	IMAR room 307
Abstract: We present the Ambrose-Singer theorem and its generalizations throughout history either with a local or global homogeneity condition. After that, we discuss the principal research program introduced by Franco Tricerri and Lieven Vanhecke and introduce the homogeneous structure tensor.

Spring 2024

Date / Time	Speaker	Title	Location
April 23, 2024 10:00	Frank Kutzschebauch Universitatea Berna	Applications of the Oka principle to Linear Algebra problems with holomorphic dependence	IMAR room 307
Abstract:
April 16, 2024 10:00	Gabriel Baditoiu IMAR	Sisteme integrabile pe varietati Poisson. Ecuatia pereche Lax	IMAR room 307
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March 26, 2024 10:00	David Petcu Universitatea Bucuresti	Complex surfaces of Kodaira class VII_0 and generalised Inoue manifolds, II	IMAR room 307
Abstract:
March 19, 2024 10:00	David Petcu Universitatea Bucuresti	Complex surfaces of Kodaira class VII_0 and generalised Inoue manifolds	IMAR room 307
Abstract: The first part is fairly introductory: we quickly survey the classification of minimal compact complex surfaces in Kodaira's class VII_0. Next, we introduce a new class of compact complex (non-Kaehler) manifolds, called "Generalized Inoue manifolds". For these, we compute some of their topological and analytic invariants: we will also discuss about the natural metrics these manifolds can have.
March 12, 2024 10:00	Rares Stan IMAR	Spectral convergence of the Dirac operator on typical hyperbolic surfaces of high genus	IMAR room 307
Abstract: We study the Dirac spectrum of typical hyperbolic surfaces of finite area, equipped with a nontrivial spin structure (so that the Dirac spectrum is discrete). For random Weil-Petersson surfaces of large genus $g$ with $o(\sqrt(g))$ cusps, we prove convergence of the spectral density to the spectral density of the hyperbolic plane, with quantitative error estimates. This result implies upper bounds on spectral counting functions and multiplicities, as well as a uniform Weyl law, true for typical hyperbolic surfaces equipped with any nontrivial spin structure.
January 30, 2024 10:00	Cornelia Vizman Timisoara	Dual pairs of momentum maps and coadjoint orbits of diffeomorphism groups	IMAR room 307
Abstract: Mutually completely orthogonal actions on a symplectic manifold yield dual pairs of momentum maps (in the sense of Weinstein). We review several such dual pairs for diffeomorphism group actions: the Marsden-Weinstein ideal fluid dual pair, the Holm-Marsden EPDiff dual pair, and a recent dual pair involving the group of volume preserving diffeomorphisms. Coadjoint orbits of diffeomorphism groups can be obtained via symplectic reduction in these dual pairs.
January 9, 2024 10:00	Costin Vilcu IMAR	Teorema lui Steinitz	IMAR room 307
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Fall 2023

Date / Time	Speaker	Title	Location
December 19, 2023 10:00	Liana David IMAR	Clasificarea metricilor Einstein generalizate impare peste grupuri Lie 3-dimensionale, partea III	IMAR room 307
Abstract: Voi prezenta cateva rezultate despre algebre Lie de dimensiune 3, necesare pentru calculul tensorului Ricci introdus in expunerile anterioare. Expunerea este independenta de cele doua expuneri anterioare, si contine rezultate demonstrate de catre V. Cortes si D. Krutsche (2022).
December 12, 2023 10:00	Liana David IMAR	Clasificarea metricilor Einstein generalizate impare peste grupuri Lie 3-dimensionale, partea II	IMAR room 307
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December 5, 2023 10:00	Liana David IMAR	Clasificarea metricilor Einstein generalizate impare peste grupuri Lie 3-dimensionale	IMAR room 307
Abstract: Voi începe cu o scurtă descriere a unor noţiuni de bază despre metrici generalizate pe algebroizi Courant arbitrari (conexiuni generalizate Levi-Civita, operatori de divergenţă, tensorul Ricci). Apoi voi exemplifica teoria pentru algebroizi Courant exacti impari stâng invarianţi peste grupuri Lie de dimensiune arbitrară. După ce voi reaminti pe scurt clasificarea algebrelor Lie de dimensiune 3, voi prezenta o clasificare pentru metricile Einstein generalizate pe astfel de algebroizi Courant, când grupul Lie are dimensiune 3. Lucrare în colaborare cu Vicente Cortes (vezi arXiv:2311.00380).
October 13, 2023 10:00	Cipriana Anghel IMAR	The spectrum of the Dirac operator on degenerating Riemannian surfaces	IMAR room 307
Abstract: We study the behavior of the spectrum of the spin Dirac operator on degenerating families of Riemannian surfaces, when the length of a simple closed geodesic shrinks to zero. We work under the hypothesis that the spin structure along the pinched geodesic is non-trivial. It is well-known that the spectrum of an elliptic differential operator on a compact manifold varies continuously under smooth perturbations of the metric. The difficulty of our problem arises from the non-compactness of the limit surface, which is of finite area with two cusps.

Spring 2023

Date / Time	Speaker	Title	Location
July 18, 2023 10:00	Victor Nistor Metz	Some topics on analysis on manifolds with bounded geometry	IMAR room 307
Abstract:
July 11, 2023 10:00	Léo Bénard Gottingen / Marsilia	Combinatorial zeta functions counting triangles	IMAR room 307
Abstract: In a joint work with Yann Chaubet, Nguyen Viet Dang and Thomas Schick, we read various topological invariants, such as (L2)-Betti numbers and linking numbers, in special values of some combinatorial zeta functions.
June 20, 2023 10:00	Florin Belgun IMAR	Olonomie riemanniană şi Weyl speciale	IMAR room 307
Abstract: Împreuna cu Brice Flamencourt si Andrei Moroianu, studiem varietătile riemanniene compacte, cu olonomie specială (strict inclusă in SO(n)) şi admitand o structură Weyl inchisă (ne-exactă) deasemenea cu olonomie specială. Aceasta structură Weyl este de fapt conexiunea Levi-Civita a unei metrici conform echivalente cu cea initială, definită insă doar pe acoperirea universală (daca ambele conexiuni corespund la metrici conform echivalente, definite pe varietatea compactă, problema este clasică). Obtinem o caracterizare geometrică a cestor varietati in functie de tipurile de olonomie ce pot apărea.
May 30, 2023 10:00	Rareş Stan IMAR	Funcţia Zeta Selberg pentru limite de operatori Dirac	IMAR room 307
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May 23, 2023 10:00	Mihai Pavel IMAR	Spaţii de moduli de fibrate vectoriale II	IMAR room 307
Abstract: Vom continua introducerea in teoria spaţiilor de moduli de fibrate vectoriale pe varietăţi complexe.
May 17, 2023 (N.B.: Wednesday) 10:00	Claude Warnick Cambridge	Singular limits of hyperbolic PDE and Effective Field Theories	IMAR room 307
Abstract: Often in a physical problem there are some degrees of freedom that we treat as unobservable because the energy required to excite them is much greater than the energy scale of the problem.These unobservable degrees of freedom can still affect the physics that we do observe at subleading order. A tool that is often used by physicists to study this is the machinery of effective field theory (EFT). An EFT is a formal expansion in some small parameter, raising important questions about how one should `solve? such an expansion and whether (and in what sense) the solutions approximate the underlying problem. In this talk I will discuss a paper with Harvey Reall in which we studied an EFT for a model PDE and explained how to address the questions that can arise.
May 9, 2023 10:00	Mihai Pavel IMAR	Spaţii de moduli de fibrate vectoriale	IMAR room 307
Abstract: Vom face o scurtă introducere in teoria spaţiilor de moduli de fibrate vectoriale pe varietăţi complexe. Printre altele, vom prezenta corespondenţa (Kobayashi-Hitchin) dintre conexiunile Yang-Mills şi structurile olomorfe stabile pe un fibrat neted fixat, iar apoi vom discuta consecinţele ei la nivelul spaţiilor de moduli care apar. În final vom prezenta câteva probleme deschise şi direcţii de cercetare legate de studiul acestor spaţii de moduli in cadrul geometriei Kähler şi non-Kähler.
April 25, 2023 10:00	Andrei Moroianu Paris	Closed 1-Forms and Twisted Cohomology	IMAR room 307
Abstract: We show that the first twisted cohomology group associated to closed 1-forms on compact manifolds is related to certain 2-dimensional representations of the fundamental group. In particular, we construct examples of nowhere-vanishing 1-forms with non-trivial twisted cohomology. (joint with Mihaela Pilca).
April 4, 2023 10:00	Cipriana Anghel-Stan IMAR	Non-local coefficients in the heat asymptotics for real powers of Laplacians	IMAR room 307
Abstract: We prove that some of the heat coefficients in the small-time asymptotic expansion of e^{-t \Delta^r} are non-local, where r \in (0,1), and \Delta is a Laplace-type operator over a compact Riemannian manifold. Furthermore, for r=1/2 we give a conceptual interpretation of the heat kernel of \Delta^r on a certain heat space M_{heat}. More precisely, $M_{heat}$ is obtained by the standard blow-up of the diagonal at time {t=0} inside M \times M \times [0, \infty).

Fall 2022

Date / Time	Speaker	Title	Location
December 13, 2022 10:00	Anda Degeratu Stuttgart	Geometria resolutiilor crepante de Calabi-Yau orbifolds	IMAR room 307
Abstract: În această expunere voi oferi o prezentare generală a unuia dintre proiectele mele de cercetare pe termen lung, în care examinez geometria anumitor varietati Calabi-Yau. Aceste varietăti sunt rezoluţii crepante de orbifolduri Calabi-Yau. Metodele mele de studiu implică o interacţiune între metodele geometrice, algebrice şi analitice.
November 22, 2022 10:00	Victor Vuletescu Bucharest	Product of LCK manifolds (II)	IMAR room 307
Abstract: It is an open question whether the product of two compact complex manifolds of LCK type does admits an LCK metric; conjecturally, the answer should be negative. In this talk, we prove that the product of any of the LCK manifolds known so far with a compact complex manifold never admits an LCK metric. This is work in progress with L. Ornea and M. Verbitsky.
October 25, 2022 10:00	Radu Pantilie Bucharest	Despre automorfisme infinitezimale pe G-varietati	IMAR room 307
Abstract: Studiem spatiile (locale) de orbite ale automorfismelor infinitezimale pe G-varietati riemanniene, cu un accent pe cazurile G=G2 si G=Spin(7) (arXiv:2105.07177).
October 18, 2022 10:00	Liana David Bucharest	Structuri pseudo-Kähler generalizate de tip B_n (partea a doua)	IMAR room 307
Abstract: Dupa o scurta recapitulare a materialului pe care l-am prezentat in luna iulie (despre algebroizi Courant de tip B_n, structuri complexe generalizate de tip B_n si metrici generalizate), voi defini notiunea de structura pseudo-Kähler generalizata de tip B_n. Voi exprima o astfel de structura in termeni de campuri tensoriale ('componente') pe baza algebroidului Courant. Voi da exemple stang invariante de astfel de structuri peste grupuri Lie de dimensiune 2, 3 si 4. De-a lungul expunerii voi explica cateva analogii intre teoria prezentata aici si teoria structurilor Kähler generalizate clasice (pe spatii tangente generalizate TM \oplus T*M).
October 11, 2022 10:00	Vlad Marchidanu Bucharest	Coomologie echivariantă şi formula Duistermaat-Heckman	IMAR room 307
Abstract: Voi prezenta câteva rezultate clasice. În primul rând, voi reaminti definiţia coomologiei echivariante a unei varietăţi pe care acţionează un grup topologic. Voi schiţa apoi demonstraţia teoremei echivariante de Rham, care permite calculul coomologiei echivariante pentru acţiuni de grupuri Lie compacte folosind modelul Weil sau, echivalent, modelul Cartan. Apoi voi prezenta în contextul coomologiei echivariante formula Duistermaat-Heckman, care permite calculul integralelor formelor echivariant închise folosind doar mulţimea punctelor fixe. Voi prezenta şi o aplicaţie recentă a formulei Duistermaat-Heckman: demonstraţia algebricităţii volumului normalizat al unei varietăţi Sasaki în raport cu o metrică Calabi-Yau pe conul său Kähler.

Spring 2022

Date / Time	Speaker	Title	Location
July 19, 2022 10:00	Louis Ioos Marburg	Canonical Kähler metrics and quantization	IMAR room 307
Abstract: The search for canonical Kähler metrics can be understood as an attempt to extend the uniformization theorem for Riemann surfaces to complex manifolds of any dimension. In this talk, I will explain the key role played by quantization methods in this program. This is based on a project in collaboration with Leonid Polterovich.
July 5, 2022 10:00	Liana David Bucharest	Structuri pseudo-Kähler generalizate de tip B_n	IMAR room 307
Abstract: Voi reaminti pe scurt relaţia dintre geometria Kähler generalizată pe algebroizi Courant exacti şi geometria bi-Hermitiană şi, de asemenea, definiţia unui algebroid Courant exact impar. Voi defini noţiunile de structură pseudo-Hermitiană şi pseudo-Kähler generalizată de tip B_n pe un algebroid Courant exact impar E. Cand E este în forma standard, voi exprima aceste structuri în termeni de câmpuri tensoriale clasice definite pe baza lui E. Voi da exemple stâng invariante peste grupuri Lie de dimensiune 2, 3 sau 4. Rezultatele sunt în colaborare cu Vicente Cortés.
May 31, 2022 10:00	Victor Vuletescu Bucharest	Product lcK manifolds	IMAR room 307
Abstract: It is an open question whether the product of two compact complex manifolds of LCK type does admits an LCK metric; conjecturally, the answer should be negative. In this talk, we prove that the product of two LCK surfaces never admits an LCK metric and prove several restrictions for the product X\times Y of compact LCK manifolds X and Y to admit an LCK metric. This is work in (very early) progress with L. Ornea and M. Verbitsky.
May 24, 2022 10:00	Costin Vilcu IMAR	Simple Closed Quasigeodesics on Tetrahedra	Zoom
Abstract: Pogorelov proved in 1949 that every convex polyhedron has at least three simple closed quasigeodesics. Whereas a geodesic has exactly π surface angle to either side at each point, a quasigeodesic has at most π surface angle to either side at each point. Pogorelov's existence proof did not suggest a way to identify the three quasigeodesics, and it is only recently that a finite algorithm has been proposed. Here we identify three simple closed quasigeodesics on any tetrahedron: at least one through 1 vertex, at least one through 2 vertices, and at least one through 3 vertices. The only exception is that isosceles tetrahedra have simple closed geodesics but do not have a 1-vertex quasigeodesic. We also identify an infinite class of tetrahedra that each have at least 34 simple closed quasigeodesics. This is recent joint work with Joseph O'Rourke (Smith College, USA).
May 17, 2022 10:00	Andrei Moroianu Paris	Conformal vector fields on lcK manifolds	IMAR room 307
Abstract: It is well known that on compact Kähler manifolds every conformal vector field is Killing (Lichnerowicz) and every Killing vector field is holomorphic. In this talk I will extend these results to the locally conformally Kähler setting. More precisely, I will show that any conformal vector field $\xi$ on a compact lcK manifold is Killing with respect to the Gauduchon metric, and if the Kähler cover of the manifold is neither flat, nor hyperkähler, then $\xi$ is holomorphic. This is joint work with Mihaela Pilca.
March 29, 2022 10:00	Zakarias Sjöström Dyrefelt Aarhus	Constant scalar curvature and Kähler manifolds with nef canonical bundle	Zoom
Abstract: Given a compact Kähler manifold it is a classical question whether it admits a Kähler metric of constant scalar curvature (cscK metric for short). In this talk we prove that there always exist cscK metrics on compact Kähler manifolds with nef canonical bundle, thus on all smooth minimal models, and also on the blowup of any such manifold. This confirms an expectation of Jian-Shi-Song and extends the seminal results of Aubin and Yau, giving a large class of new examples of cscK manifolds. As a byproduct we show that the connected component of the automorphism group of any compact Kähler manifold with nef canonical bundle is either trivial or a complex torus. The tools used are from the variational approach in Kähler geometry, and some related results on stability thresholds and Donaldson's J-equation are discussed along the way.
March 22, 2022 10:00	Liviu Ornea Bucuresti	Toate varietăţile Hopf sunt LCK	IMAR sala 307
Abstract: Demostrăm că orice cât al lui $C^n\backslash 0$ printr-o contracţie olomorfă cu centrul 0 este LCK (colaborare cu Misha Verbitsky).
March 15, 2022 10:00	Adriano Tomassini Parma	TBA	Zoom
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March 8, 2022 10:00	Sorin Dumitrescu Nisa	Holomorphic foliations and transverse Cartan geometry	Zoom
Abstract:This talk will present the foliated aspect of Cartan's geometries (connections) which are geometrical structures infinitesimally modeled on homogeneous spaces. After an introduction of the classical framework providing motivations, we will show classification results for holomorphic foliations with transversal Cartan geometries on rationally connected varieties and on Calabi-Yau manifolds. This is based on a joint work with Indranil Biswas (TIFR, Mumbai).
February 15, 2022 10:00	Francesco Pediconi Florenţa	Collapsed ancient solutions of the Ricci flow on compact homogeneous spaces	Zoom
Abstract:The Ricci flow (RF) is a geometric PDE that evolves a Riemannian metric in the direction of its Ricci tensor. Solutions that are defined for any negative time are called ancient, and they arise as blow-up limits near singularities. In this talk, we review some classical facts concerning the RF on compact homogeneous spaces and we present a general existence theorem for collapsed ancient solutions. Furthermore, we show that all our solutions converge in the Gromov-Hausdorff topology, under a suitable rescaling, to an Einstein metric on the base of a torus fibration. As a direct consequence of this result, we illustrate a series of examples. This is joint work with S. Sbiti.

Fall 2021

Date / Time	Speaker	Title	Location
February 1, 2022 10:00	Andrea Sambusetti Roma	Finiteness of hyperbolic groups with bounded entropy	Zoom
Abstract:I will present a new finiteness theorem: there are only finitely many torsionless groups G acting discretely by isometries on some delta-hyperbolic space X with entropy Ent(X) < E and diameter of the quotient space G\X less than D. I will explain the genesis of the result, which dates back to the work of Heintze, Cheeger and Gromov, declining it in different forms: for 3-manifolds, for general non-positively curved n-manifolds, for Gromov hyperbolic spaces and groups. The main tool behind it is a new, "curvature-free" volume comparison inequality a-la Bishop-Gromov, which only needs an upper bound of entropy and diameter. (This is a joint work with G. Besson, G. Courtois and S. Gallot, see arXiv:2109.13025)
January 25, 2022 10:00	Brice Flamencourt Orsay	Cauchy spinors on 3-manifolds	Zoom
Abstract:The so-called Cauchy spinors arise naturally when one considers the restriction of a parallel spinor on a spin-manifold $Z$ to an oriented hypersurface $M$ of $Z$. The covariant derivative of such a restriction in the direction of $X \in TM$ is given by the Clifford multiplication by $-A(X)/2$ where $A$ is the second fundamental form of the hypersurface. Then, we can consider more generally the spinors satisfying this last condition on a manifold $M$, with $A$ being an arbitrary symmetric endomorphism field. This is what we call Cauchy spinors. In dimension three, the study of Cauchy spinors on simply connected manifolds is equivalent to the flatness of a connection, which can be rewritten as an equation on the endomorphism field $A$. Since this is a non-linear differential equation, it is still hard to fully understand the structure of this spinors space, even in the simple case of the round sphere $\SS^3$. However, we can give some structure results on manifolds with positive curvature. Moreover, we can use the Lie group structure of $\SS^3$ in order to make explicit computations in this case.
December 21, 2021 10:00	Sergiu Moroianu IMAR	Introducere in geometria spinoriala in dimensiuni 3 si 4, Part II	Zoom
Abstract:
December 14, 2021 10:00	Sergiu Moroianu IMAR	Introducere in geometria spinoriala in dimensiuni 3 si 4	Zoom
Abstract:Expunerea va fi o introducere in lumea spinorilor. Voi construi grupurile Spin(3) si Spin(4) si reprezentarile lor spinoriale. Orice 3-varietate Riemaniana orientata M este inzestrata cu structuri Spin. Daca M este o hipersuprafata intr-o 4-varietate Riemaniana spin X, putem restrange spinori de la X la M. Cand X admite spinori paraleli nenuli, curbura sa Ricci se anuleaza iar metrica este (anti)auto-duala; in plus, metrica lui M si a doua sa forma fundamentala satisfac doua ecuatii de constragere obtinute prin contractarea ecuatiilor Gauss si Codazzi, iar restrictia spinorului paralel de pe X la M este un asa-numit spinor Cauchy. Vom studia problema Cauchy de extindere a unui spinor Cauchy de pe M la un spinor paralel pe X.
December 7, 2021 10:00	Ovidiu Preda IMAR	Vaisman theorem for locally conformally Kähler spaces	Zoom
Abstract:Vaisman's theorem states that any locally conformally Kähler metric on a compact complex manifold which admits a Kähler metric is, in fact, globally conformally Kähler. We extend this theorem to compact (singular) complex spaces which are locally irreducible. We also present an example which shows that the additional assumption of local irreducibility cannot be dropped.
November 9, 2021 10:00	Liana David IMAR	T-dualitate pentru algebroizi Courant tranzitivi	Zoom
Abstract: Voi incepe cu o scurta prezentare a teoriei conexiunilor generalizate si a operatorilor de generare Dirac pentru algebroizi Courant tranzitivi. Rezultatul principal al expunerii este o T-dualitate pentru algebroizi Courant tranzitivi, care generalizeaza T-dualitatea lui Cavalcanti si Gualtieri in cazul exact. Voi demonstra diverse proprietati ale algebroizilor Courant tranzitivi aflati in T-dualitate si un rezultat general de existenta a unui T-dual pentru un algebroid Courant tranzitiv dat. Ca exemplificare a teoriei, voi demonstra ca T-dualul unui algebroid Courant heterotic este tot heterotic. Rezultate obtinute in colaborare cu Vicente Cortes (arxiv:2101.07184).

Spring 2021 - Joint GAP - Geometry seminar

Date / Time	Speaker	Title	Location
May 11, 2021 10:00	Adrien Boulanger Bologna	Spectral theory and linking forms	Zoom
Abstract: We shall discuss the notion of linking form, closely related to the one of linking number, with a special focus on its interaction with spectral theory. We will start with basic definitions and examples, coming back to Gauss' first definitions. (Work in progress with Gilles Courtois).
April 6, 2021 10:00	Calin Lazaroiu IFIN	Spinor structures, G-structures and Fierz potentials	Zoom
Abstract:
March 24, 2021 17:00	Carlos Shahbazi Alonso Hamburg	Mathematical Supergravity and its applications to differential geometry	Zoom
Abstract:
March 16, 2021 10:00	Sergiu Moroianu IMAR Bucharest	The Gauss-Bonnet formula on polyhedra	Zoom
Abstract: https://arxiv.org/abs/2011.06538
February 16, 2021 10:00	Adrien Boulanger Pisa	A Cheeger like inequality for 1-forms	Zoom
Abstract: Work in collaboration with Gilles Courtois
February 9, 2021 10:00	Patrick Popescu-Pampu Lille	The Combinatorics of Plane Curve Singularities	Zoom
Abstract: Ever since Newton introduced the first combinatorial object in the study of singularities of plane curves, later called the "Newton polygon", several trees -- i.e. connected graphs without cycles -- were introduced in order to completely encode the combinatorial structure of such a singularity. I will explain how, starting from some Newton polygons associated to a deeper and deeper "microscopic" study of the initial singularity, one can construct a special simplicial bidimensional complex -- a lotus -- in which all these trees embed. One can thus visualize the relations between all of them simultaneously, in contrast with the previous situation, in which there existed only algorithms relating two such trees. My talk will consist of an introduction to the first chapter of "Handbook of Geometry and Topology of Singularities I", recently written in collaboration with Evelia Garcia Barroso and Pedro Gonzalez Perez.
January 27, 2021 17:00	Gaetan Borot Berlin	Double Hurwitz numbers, topological recursion and ELSV-type formulas	Zoom
Abstract:
January 20, 2021 17:00	Carlos Shahbazi Alonso Hamburg	Heterotic solitons on four-manifolds	Zoom
Abstract:

Fall 2020

Date / Time	Speaker	Title	Location
November 24, 2020 10:00-11:30	Daniele Angella Florenţa	On cohomogeneity one Hermitian non-Kähler manifolds	Zoom
Abstract: We study Hermitian manifolds with a compact Lie group action by holomorphic isometries with principal orbits of codimension one. In particular, we focus on a special class of these manifolds constructed by following Bérard-Bergery. We compute the Chern-Ricci curvatures and we derive the Chern-Einstein equation. We show that these metrics are always locally conformally Kähler, and we characterize other special Hermitian conditions, such as balanced, Gauduchon, pluriclosed, Kähler-like, Vaisman. The talk is a joint collaboration with Francesco Pediconi.
November 17, 2020 10:00-11:30	Liana David IMAR	(TE)-structuri peste F-varietati 2-dimensionale	Zoom
Abstract:
November 10, 2020 10:00-11:30	Iulia Plesca UAIC Iaşi	Algebraic Heun Operators	Zoom
Abstract: Consider the Heun operator, the second order differential operator with four regular singular points. We are interested to find conditions for which the ordinary linear differential equation H(y)=0 has a full set of algebraic solutions. In this case, we see the corresponding Heun operators as pull-backs by Belyi functions of algebraic hypergeometric operators. We search for these functions by finding their corresponding dessin d?enfant. We find some infinite families of dessins d?enfants parametrized by the number of edges.
November 3, 2020 10:00-11:30	Cipriana Anghel IMAR	Weyl's law about counting the eigenvalues of a Laplacian	Zoom
Abstract: We present a classical result (due to Weyl, Minaksisundaram-Pliejel, Karamata, etc.) concerning the number of eigenvalues of a Laplacian. More precisely, we consider the Laplacian H=\nabla^* \nabla in a vector bundle E with metric and compatible connection over a closed manifold M. Let N(k) be the number of eigenvalues of H that are less than k. The aim is to describe the asymptotic behavior of this function as k grows to infinity.
October 20, 2020 14:00-15:30	Costin Vilcu IMAR	Tailoring for Every Body: Reshaping Convex Polyhedra II	Zoom
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October 13, 2020 14:00-15:30	Costin Vilcu IMAR	Tailoring for Every Body: Reshaping Convex Polyhedra	Zoom
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Spring 2020

Date / Time	Speaker	Title	Location
July 21, 2020 14:00-15:30	Corina Ciobotaru Fribourg	Classical homogeneous dynamics in a non-linear setting	Zoom
Abstract: The automorphisms group of a bi-regular tree contains a rich class of non-linear subgroups G that still share the good properties of the linear ones. Given that, classical questions from homogeneous dynamics can be examined and proved. For example, if H is a discrete subgroup of G, recent results show there is a classification of ergodic probability measures on G / H that are invariant under horospherical subgroups. When H is moreover a cocompact lattice, the horospherical action is uniquely ergodic. Or when H is a geometrically finite lattice quantitative recurrence and equidistribution related to the above probability measures on G / H hold true. This is a joint project with Vladimir Finkelshtein and Cagri Sert.
July 14, 2020 10:00-11:30	Adrien Boulanger Marseille	The Dirichlet random walk	Zoom
Abstract: Let M \to M_0 a Galoisian Riemannian covering from M to M_0 with deck group \Gamma. Being given an 'initial point' o \in M we define recursively a stochastic process on M as follows: pick countably many independent random variables (p_i)_{\in \mathbb{N}^*} following the law given by the (renormalized) Riemannian measure on M_0. Now construct a piecewise geodesic path by relating o with p_1 and each p_i with p_{i+1} with the (almost surely unique) minimizing geodesic g_i having them as endpoints. Concatenating the n-thn first geodesic segments g_0... g_{n-1} together gives rise to a piecewise geodesic of M_0. Such a path being in particular continuous, one can lift it to M to get a random sequence of points on M (the endpoint of the lift of the piecewise geodesic given by g_0... g_{n-1}). This talk will focus on proving an analogous of Kesten's criterion in this case : \Gamma is amenable if and only if the associated Markov operator has a spectral gap. The proof is analytical, knowledge in probability theory is not required.
June 16, 2020 10:00-11:30	Alexandra Otiman IMAR	Probleme variationale in geometria conforma	Zoom
Abstract: We study the Euler-Lagrange equation for several natural functionals defined on a conformal class of almost Hermitian metrics, whose expression involves the Lee form of the metric. We show that Gauduchon metrics are the unique extremal metrics of the functional corresponding to the norm of the Lee form?s codifferential. Moreover, in the spirit of Gauduchon?s celebrated result, we prove that in any given conformal class, there exists a unique (up to scalar multiplications) metric with special properties. This is joint work with D. Angella, N. Istrati and N. Tardini.
June 9, 2020 10:00-11:30	Miron Stanciu IMAR	Compatibility between non-Kähler structures on complex (nil)manifolds	Zoom
Abstract:
June 9, 2020 10:00-11:30	Cipriana Anghel IMAR	Heat kernel asymptotics for real powers of Laplacians	Zoom
Abstract: I will describe the small-time heat kernel asymptotics for real powers r \in (0,1) of a generalised Laplacian on sections of a vector bundle over a compact Riemannian manifold.
February 4, 2020 10:00-11:30	Liviu Ornea IMAR si FMI	Coomologia algebrelor Lie nilpotente si clasificarea nilvarietatilor LCK	Sala 307
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January 21, 2020 10:00-11:30	Olivier Guichard Universitatea Strasbourg	Teichmüller spaces and their generalizations	Sala 307
Abstract: This talk will be devoted to present the Teichmüller space (ie the universal cover of the Riemann moduli space) and the different points of view (analytical, dynamical, homological, combinatorical) on it that have been developed the last thirty years. In turn, these different approaches give rise to new family of spaces called generalized Teichmüller spaces. If time permits, results of the speaker and his collaborators will be mentioned.

Fall 2019

Date / Time	Speaker	Title	Location
December 10, 2019 10:00-11:30	Costin Vilcu IMAR	Diametral points of convex bodies	Sala 307
Abstract: Based on this preprint.

December 3, 2019 10:00-11:30	Gabriel Baditoiu IMAR	Actiuni tranzitive si metrici Einstein omogene pe hiperboloizi	Sala 307
Abstract:
November 26, 2019 10:00-11:30	Andrei Moroianu CNRS Orsay	Metric connections with parallel skew-symmetric torsion	Sala 307
Abstract: In this talk I will present some results, obtained in collaboration with Uwe Semmelmann and Richard Cleyton, about the structure of Riemannian manifolds carying a metric connection with parallel skew-symmetric (non-vanishing) torsion. These objects appear naturally in different geometric contexts, e.g. on naturally reductive homogeneous spaces, on Sasakian and 3-Sasakian manifolds, or on nearly Kähler and nearly parallel G_2 manifolds. Cleyton and Swann have classified them in the case of irreducible holonomy. In the reducible case, I will show that the manifold is the total space of a Riemannian submersion with totally geodesic homogeneous fibres over a Riemannian manifold which carries a metric connection with parallel skew-symmetric (possibly vanishing) torsion, and a principal bundle with parallel curvature. This result opens the way towards a possible classification of geometries with parallel skew-symmetric torsion.
November 19, 2019 10:00-11:30	Ovidiu Preda IMAR	Coverings of LCK complex spaces	Sala 307
Abstract:
November 12, 2019 10:00-11:30	Dan Burghelea Ohio State University	From topology to geometry via analytic continuation	Sala 307
Abstract:
November 5, 2019 10:00-11:30	Liana David IMAR	The Dirac generating operator of a Courant algebroid	Sala 307
Abstract:
October 29, 2019 10:00-11:30	Florin Belgun IMAR	The Matthai-Quillen construction	Sala 307
Abstract:
October 29, 2019 10:00-11:30	Sergiu Moroianu IMAR	The generalized Gauss-Bonnet theorem	Sala 307
Abstract:

Organizer: Sergiu Moroianu

Archive: