# Geometry seminar at IMAR

## Spring 2022

Date / Time Speaker Title Location
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.

## 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
Abstract:
October 13, 2020
14:00-15:30
Costin Vilcu
IMAR
Tailoring for Every Body: Reshaping Convex Polyhedra Zoom
Abstract:

## 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 (renormalised) 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) minimising geodesic g_i having them as endpoints. Concaneting 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
Abstract:
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:

Modified: 05.20.2022