Seminar on Geometry


Seminar on Geometry Spring/Fall 2023, Boğaziçi, İstanbul Time / Location: Fridays 4:00 / TB-240

Schedule of talks


TIME	SPEAKER	TITLE
Jan 16-21		The 10th GTSS Geometry-Topology Winter School Nesin Mathematics Village
Jan 27 Fri, 4:00		No Seminar
Feb 3 Fri, 4:00	Zoom link. Pass: geometry in Turkish. Meeting ID: 991 1027 7750	Spectrum of the Riemannian Laplacian on the round n-dimensional sphere
Feb 10 Fri, 4:00		Spectrum of the Riemannian Laplacian on the round n-dimensional sphere 2
Feb 17 Fri, 4:00		Minimal Surfaces and the Bernstein Problem 1 Index of Spheres as totally geodesic minimal submanifolds
Feb 24 Fri, 4:00		Minimal Surfaces and the Bernstein Problem 2 Jacobi Fields on Spheres
Mar 4-5	Conference	SCGAS Irvine, CA
Mar 10 Fri, 4:00		No Seminar
Mar 17 Fri, 4:00		Minimal Surfaces and the Bernstein Problem 3 Negative definite index form
Mar 24 Fri, 4:00		Minimal Surfaces and the Bernstein Problem 4 Killing fields on the sphere
Mar 31 Fri, 4:00		Minimal Surfaces and the Bernstein Problem 5 Using Killing fields on the sphere to find nullity
Apr 7 Fri, 4:00		Minimal Surfaces and the Bernstein Problem 6 An extrinsic rigidity theorem
Apr 13 Thu, 4:30	Jan Kotrbaty Frankfurt	An algebraic approach to inequalities in convex geometry Oberseminar Differentialgeometrie, MPIM Lecture Hall
Apr 14 Fri, 3:30	Craig van Coevering Boğaziçi	Extremal Kähler metrics and the moment map Online AG Seminar
Apr 20 Thu, 4:30	Tommaso Cremaschi Luxembourg	Geometry of some infinite-type hyperbolic 3-manifolds Oberseminar Differentialgeometrie, MPIM Lecture Hall
Apr 21 Fri, 4:00	Holiday	Ramazan Bayramı
Apr 25 Tue, 4:30	Thomas Schick Göttingen	Rigidity of scalar curvature and low regularity Oberseminar Topologie, Endenicher Allee 60, Raum 1.008
Apr 28 Fri, 3:00		Minimal Surfaces and the Bernstein Problem 7 Rigidity theorem for higher codimension
May 4 Thu, 10:30	Justin Sawon North Carolina/MPIM	Lagrangian fibrations in six dimensions Seminar Algebraic Geometry (SAG) Vivatsgasse 7, Hörsaal MPIM
4:30	Shi Wang MSU/MPIM	Eisenstein series and cusp counting in hyperbolic manifolds Oberseminar Differentialgeometrie, MPIM Lecture Hall
May 5 Fri, 3:00		Minimal Surfaces and the Bernstein Problem 8 Rigidity theorem for higher codimension 2
May 8-12	Workshop	Noncommutative Geometry and Operator Algebras Lecture hall HIM, Poppelsdorfer Allee 45, Bonn
May 11 Thu, 4:30	Thang Nguyen Uni. of Michigan	Local rigidity of boundary actions Oberseminar Differentialgeometrie, MPIM Lecture Hall
May 12 Fri, 3:00		Minimal Surfaces and the Bernstein Problem 9 Sphere rigidity theorem
May 17-19	Conference	A Complex Differential Geometry Meeting at UniTo Università degli Studi di Torino
May 24 Wed, 2:00		Dies Academicus
May 26 Fri, 4:00		No Seminar
Jun 2 Fri, 4:00	Holiday	Pfingstferien
Jun 9 Fri, 4:00		Minimal Surfaces and the Bernstein Problem 10 TBA
Jun 16 Fri, 4:00		Minimal Surfaces and the Bernstein Problem 11 Index and nullity of a minimal surface
Jun 23 Fri, 4:00		Minimal Surfaces and the Bernstein Problem 12 TBA
Jun 30 Fri, 4:00		Minimal Surfaces and the Bernstein Problem 13 Minimal surfaces in the 6-sphere. First and second normal bundles
Jul 7 Fri, 4:00		Minimal Surfaces and the Bernstein Problem 14 Moving frames in the 6-sphere
Jul 14 Fri, 4:00		Minimal Surfaces and the Bernstein Problem 15 TBA
Jul 17-22	Youtube	The 11th GTSS Geometry-Topology Summer School IMBM - Week 1
Jul 24-29	Videos	Summer School IMBM - Week 2
Aug 4 Fri, 4:00		Minimal Surfaces and the Bernstein Problem 16 Holomorphic curvature and torsion
Aug 7-11	Conference	Analytic Methods in Complex Geometry Münster
Aug 18 Fri, 4:00		Minimal Surfaces and the Bernstein Problem 18 Holomorphic interpretation of the Torsion
Aug 25 Fri, 4:00		Minimal Surfaces and the Bernstein Problem 19 Holomorphic Frenet equations
Sep 1 Fri, 4:00		Minimal Surfaces and the Bernstein Problem 20 Holomorphic interpretation of the Torsion
Sep 8 Fri, 4:00		No Seminar
Sep 11-16		The 12th GTSS Geometry-Topology Summer School Nesin Mathematics Village - Week 1
Sep 18-23		Summer School Week 2
Sep 29 Fri, 3:30		No Seminar
Oct 7 Fri, 3:30		Minimal varieties in higher dimensional spheres 1 Introduction. Riemannian vector bundles.
Oct 13-16	Conference	Symmetry and shape Santiago de Compostela, Spain
Oct 21 Fri, 3:30		Minimal varieties in higher dimensional spheres 2 Laplace operator
Oct 28 Fri, 3:30		Minimal varieties in higher dimensional spheres 3 Geometry of immersed submanifolds
Nov 4 Fri, 3:30		Minimal varieties in higher dimensional spheres 4 Curvature of the normal bundle
Nov 8 Tue, 2:15	Oberseminar Global Analysis and Operator Algebras	On special submanifolds of the Page space Location: Endenicher Allee 60, Room 0.008
Nov 11 Fri, 3:30		Minimal varieties in higher dimensional spheres 5 Mean curvature and minimal varieties
Nov 18 Fri, 4:00		Minimal varieties in higher dimensional spheres 6 The case of Kähler manifolds
Nov 25 Fri, 4:00		Minimal varieties in higher dimensional spheres 7 The case of Kähler manifolds 2
Dec 2 Fri, 4:00		Minimal varieties in higher dimensional spheres 8 The case of Kähler manifolds 3
Dec 9 Fri, 4:00		Minimal varieties in higher dimensional spheres 9 An extension of the Synge Lemma
Dec 16 Fri, 4:00		Minimal varieties in higher dimensional spheres 10 Laplacian of the Shape Operator
Dec 23 Fri, 4:00		Minimal varieties in higher dimensional spheres 11 Mean curvature and minimal varieties
Dec 30 Fri, 4:00		Minimal varieties in higher dimensional spheres 12 Curvature of the normal bundle
Jan 6 Fri, 4:00		Minimal varieties in higher dimensional spheres 13 Projection of parallel vector fields as the Kernel of the Jacobi operator

Abstracts/Notlar

Spectrum of the Riemannian Laplacian on the round n-dimensional sphere

Using the spherical harmonic functions we understand the eigenvalues and eigenvectors of the Laplacian on the round 2-sphere also the general n-sphere. [1] contains explicit descriptions of the eigenvalues and eigenvectors of the standard basic manifolds including the n-sphere. Of historical interest is the treatment in what is arguably the first textbook on physics by Tait and Thomson. The latter (a.k.a. Lord Kelvin) used it to estimate the age of the sun. Inaccurately, but not due to errors in the mathematics, thermonuclear reactions hadn’t yet been discovered.[MO] We will be using the following resources.

References:

Berger, Marcel; Gauduchon, Paul; Mazet, Edmond. - Le spectre d'une variété riemannienne.
Lecture Notes in Mathematics, Vol. 194 Springer-Verlag, Berlin-New York 1971 vii+251 pp.

Piotr Hajlasz – Functional Analysis notes.

Minimal Surfaces and the Bernstein Problem

In this learning seminar series, we will give an introduction to minimal submanifolds of the higher dimensional spheres. In particular we give estimates on the index of the Jacobi operator. Talk about applications on the Plateau's problem and Bernstein conjecture.

Ingredients of the individual seminars are as follows:

B-1: Index of Spheres as totally geodesic minimal submanifolds.

B-2: Jacobi fields on totally geodesic minimal spheres in higher dimensional spheres.

B-3: Negative definite index form.

B-4: Killing Fields on the sphere.

B-5: Using Killing Fields on the sphere to find nullity.

B-6: An extrinsic rigidity theorem.

B-7: Rigidity theorem for higher codimension.

B-8: Rigidity theorem for higher codimension 2.

B-9: Sphere rigidity theorem.

S-10: Laplacian of the Shape Operator.

S-11: Mean curvature and minimal varieties.

S-12: Curvature of the normal bundle.