Date / Time | Speaker | Title | Location | |
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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 varietati sunt rezoluții crepante de orbifolduri Calabi-Yau. Metodele mele de studiu implică o interacțiune între metodele geometrice, algebrice și analitice.
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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-Kahler 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 și formula Duistermaat-Heckman | IMAR room 307 | |
Abstract: Voi prezenta câteva rezultate clasice. În primul rând, voi reaminti definiția coomologiei echivariante a unei varietăți pe care acționează un grup topologic. Voi schița apoi demonstrația teoremei echivariante de Rham, care permite calculul coomologiei echivariante pentru acțiuni 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 mulțimea punctelor fixe. Voi prezenta și o aplicație recentă a formulei Duistermaat-Heckman: demonstrația algebricității volumului normalizat al unei varietății Sasaki în raport cu o metrică Calabi-Yau pe conul său Kähler. |
Date / Time | Speaker | Title | Location | |
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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 relația dintre geometria Kähler generalizată pe algebroizi Courant exacti și geometria bi-Hermitiana, și, de asemenea, definiția unui algebroid Courant exact impar. Voi defini noțiunile de structura pseudo-Hermitiana și 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 varietățile Hopf sînt LCK | IMAR sala 307 | |
Abstract: Demostrăm că orice cît al lui $C^n\backslash 0$ printr-o contracție olomorfă cu centrul 0 este LCK (colaborare cu Misha Verbitsky). | ||||
March 15, 2022 10:00 |
Adriano Tomassini Parma |
TBA | Zoom | |
Abstract: | ||||
March 8, 2022 10:00 |
Sorin Dumitrescu Nisa |
Holomorphic foliations and tranverse 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. |
Date / Time | Speaker | Title | Location | |
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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). |
Date / Time | Speaker | Title | Location | |
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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:
Modified: 11.22.2022