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BT 86.972 716.845 Td /F2 24.0 Tf [(Recent advances on scalar curvature problems)] TJ ET
BT 283.199 677.782 Td /F2 18.0 Tf [(Events for:)] TJ ET
BT 183.929 656.355 Td /F2 18.0 Tf [(Monday, June 27th - Friday, July 1st)] TJ ET
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BT 268.183 620.083 Td /F2 14.0 Tf [(Monday, June 27th)] TJ ET
BT 36.266 602.206 Td /F1 12.0 Tf [(9:00am)] TJ ET
BT 84.529 601.601 Td /F2 12.0 Tf [(Lorenzo Mazzieri - SCGP 102)] TJ ET
BT 84.529 572.230 Td /F2 12.0 Tf [(Speaker: )] TJ ET
BT 133.525 572.230 Td /F1 12.0 Tf [(Lorenzo Mazzieri )] TJ ET
BT 84.529 543.430 Td /F2 12.0 Tf [(Title: )] TJ ET
BT 115.525 543.430 Td /F1 12.0 Tf [(Geometric inequalities and potential theory )] TJ ET
BT 84.529 514.745 Td /F2 12.0 Tf [(Abstract: )] TJ ET
BT 136.177 514.745 Td /F1 12.0 Tf [(We describe through some selected examples an approach based on potential theory )] TJ ET
BT 84.529 500.489 Td /F1 12.0 Tf [(toward the proof of relevant geometric inequalities, holding in classical and curved frameworks. )] TJ ET
BT 84.529 486.233 Td /F1 12.0 Tf [(Time permitting, we also discuss some applications of interest in general relativity, including the )] TJ ET
BT 84.529 471.862 Td /F1 12.0 Tf [(positive mass theorem and the Riemannian Penrose inequality. )] TJ ET
BT 36.266 428.782 Td /F1 12.0 Tf [(10:00am)] TJ ET
BT 84.529 428.177 Td /F2 12.0 Tf [(Christina Sormani - SCGP 102)] TJ ET
BT 84.529 398.806 Td /F2 12.0 Tf [(Speaker: )] TJ ET
BT 133.525 398.806 Td /F1 12.0 Tf [(Christina Sormani )] TJ ET
BT 84.529 370.006 Td /F2 12.0 Tf [(Title: )] TJ ET
BT 115.525 370.006 Td /F1 12.0 Tf [(Compactness and Stability Conjectures )] TJ ET
BT 84.529 341.321 Td /F2 12.0 Tf [(Abstract: )] TJ ET
BT 136.177 341.321 Td /F1 12.0 Tf [(Gromov has conjectured that a sequence of compact three dimensional Riemannian )] TJ ET
BT 84.529 327.065 Td /F1 12.0 Tf [(manifolds with nonnegative scalar curvature converges in the intrinsic flat sense to a limit space )] TJ ET
BT 84.529 312.809 Td /F1 12.0 Tf [(with generalized nonnegative scalar curvature. He has also conjectured the stability of the scalar )] TJ ET
BT 84.529 298.553 Td /F1 12.0 Tf [(torus rigidity theorem: that a sequence of three tori with scalar >-1/j has a subsequence which )] TJ ET
BT 84.529 284.297 Td /F1 12.0 Tf [(converges in the intrinsic flat sense to a flat torus. We will survey examples and results in this )] TJ ET
BT 84.529 270.041 Td /F1 12.0 Tf [(direction including joint work with Allen and Perales introducing a notion we call VADB )] TJ ET
BT 84.529 255.785 Td /F1 12.0 Tf [(convergence that has been applied by Cabrera Pacheco, Perales, and Ketterer to prove the stability )] TJ ET
BT 84.529 241.529 Td /F1 12.0 Tf [(of the scalar torus rigidity theorem. We will suggest a number of open problems applying VADB )] TJ ET
BT 84.529 227.158 Td /F1 12.0 Tf [(convergence to test both these conjectures and others. )] TJ ET
BT 36.266 184.078 Td /F1 12.0 Tf [(11:00am)] TJ ET
BT 84.529 183.473 Td /F2 12.0 Tf [(Coffee Break - SCGP Cafe)] TJ ET
BT 36.266 163.822 Td /F1 12.0 Tf [(11:30am)] TJ ET
BT 84.529 163.217 Td /F2 12.0 Tf [(Daniel Stern - SCGP 102)] TJ ET
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BT 84.529 732.214 Td /F2 12.0 Tf [(Speaker: )] TJ ET
BT 133.525 732.214 Td /F1 12.0 Tf [(Daniel Stern)] TJ ET
BT 84.529 689.014 Td /F2 12.0 Tf [(Title: )] TJ ET
BT 115.525 689.014 Td /F1 12.0 Tf [(Harmonic maps and extremal Schrodinger operators on higher-dimensional manifolds)] TJ ET
BT 84.529 645.929 Td /F2 12.0 Tf [(Abstract: )] TJ ET
BT 136.177 645.929 Td /F1 12.0 Tf [(I'll discuss recent progress on the existence theory for harmonic maps from arbitrary )] TJ ET
BT 84.529 631.673 Td /F1 12.0 Tf [(Riemannian manifolds of dimension >2 to a large class of target manifolds, including 3-manifolds )] TJ ET
BT 84.529 617.417 Td /F1 12.0 Tf [(of positive Ricci curvature and manifolds of dimension > 3 with positive isotropic curvature. As a )] TJ ET
BT 84.529 603.161 Td /F1 12.0 Tf [(special case, every Riemannian manifold \(M^n,g\) of dimension n>2 admits a family of nontrivial )] TJ ET
BT 84.529 588.905 Td /F1 12.0 Tf [(stationary harmonic maps u_k to the standard spheres S^k for k>2, smooth away from a singular )] TJ ET
BT 84.529 574.649 Td /F1 12.0 Tf [(set of dimension at most n-7 for k sufficiently large. I'll explain how these maps give rise to )] TJ ET
BT 84.529 560.393 Td /F1 12.0 Tf [(solutions of an optimization problem for Schrodinger operators related to work of Grigor'yan-)] TJ ET
BT 84.529 546.137 Td /F1 12.0 Tf [(Netrusov-Yau and Grigor'yan-Nadirashvili-Sire, generalizing to higher dimensions the )] TJ ET
BT 84.529 531.881 Td /F1 12.0 Tf [(maximization of Laplace eigenvalues on surfaces of fixed conformal type. \(Based on joint work )] TJ ET
BT 84.529 517.510 Td /F1 12.0 Tf [(with Mikhail Karpukhin.\))] TJ ET
BT 36.266 460.030 Td /F1 12.0 Tf [(12:30pm)] TJ ET
BT 84.529 459.425 Td /F2 12.0 Tf [(Lunch - SCGP Cafe)] TJ ET
BT 36.266 439.774 Td /F1 12.0 Tf [(2:00pm)] TJ ET
BT 84.529 439.169 Td /F2 12.0 Tf [(Jinmin Wang - SCGP 102)] TJ ET
BT 84.529 409.798 Td /F2 12.0 Tf [(Speaker: )] TJ ET
BT 133.525 409.798 Td /F1 12.0 Tf [(Jinmin Wang)] TJ ET
BT 84.529 366.598 Td /F2 12.0 Tf [(Title: )] TJ ET
BT 115.525 366.598 Td /F1 12.0 Tf [(Dihedral rigidity conjecture and Stoker's problem)] TJ ET
BT 84.529 323.513 Td /F2 12.0 Tf [(Abstract: )] TJ ET
BT 136.177 323.513 Td /F1 12.0 Tf [(The Stoker Conjecture states that the dihedral angles of a convex Euclidean polyhedron )] TJ ET
BT 84.529 309.257 Td /F1 12.0 Tf [(completely determine the angles of each face. In this talk, I will present my recent work joint with )] TJ ET
BT 84.529 295.001 Td /F1 12.0 Tf [(Zhizhang Xie and Guoliang Yu that answers positively to the Stoker Conjecture in all dimensions. )] TJ ET
BT 84.529 280.745 Td /F1 12.0 Tf [(Our work proves a more general dihedral rigidity theorem, which concerns the comparison of )] TJ ET
BT 84.529 266.489 Td /F1 12.0 Tf [(scalar curvature, mean curvature, and dihedral angles for convex polyhedrons, or more general, )] TJ ET
BT 84.529 252.233 Td /F1 12.0 Tf [(manifolds with polytope boundary. We use index theory on manifolds with polytope boundary and )] TJ ET
BT 84.529 237.862 Td /F1 12.0 Tf [(the Dirac operator methods.)] TJ ET
BT 36.266 180.382 Td /F1 12.0 Tf [(3:00pm)] TJ ET
BT 84.529 179.777 Td /F2 12.0 Tf [(Zhizhang Xie - SCGP 102)] TJ ET
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BT 84.529 732.214 Td /F2 12.0 Tf [(Speaker: )] TJ ET
BT 133.525 732.214 Td /F1 12.0 Tf [(Zhizhang Xie )] TJ ET
BT 84.529 703.414 Td /F2 12.0 Tf [(Title: )] TJ ET
BT 115.525 703.414 Td /F1 12.0 Tf [(On Gromov’s dihedral extremality and rigidity conjectures )] TJ ET
BT 84.529 674.729 Td /F2 12.0 Tf [(Abstract: )] TJ ET
BT 136.177 674.729 Td /F1 12.0 Tf [(Gromov’s dihedral extremality and rigidity conjectures concern comparisons of scalar )] TJ ET
BT 84.529 660.473 Td /F1 12.0 Tf [(curvature, mean curvature and dihedral angle for manifolds with corners \(and more generally )] TJ ET
BT 84.529 646.217 Td /F1 12.0 Tf [(manifolds with polyhedral boundary\). They have very interesting consequences in geometry and )] TJ ET
BT 84.529 631.961 Td /F1 12.0 Tf [(mathematical physics. The conjectures themselves can in some sense be viewed as “localizations” )] TJ ET
BT 84.529 617.705 Td /F1 12.0 Tf [(of the positive mass theorem. In this talk, I will explain some recent work on positive solutions to )] TJ ET
BT 84.529 603.334 Td /F1 12.0 Tf [(these conjectures. The talk is based on my joint papers with Jinmin Wang and Guoliang Yu. )] TJ ET
BT 36.266 560.254 Td /F1 12.0 Tf [(4:00pm)] TJ ET
BT 84.529 559.649 Td /F2 12.0 Tf [(Coffee Break - SCGP Cafe)] TJ ET
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BT 267.791 536.743 Td /F2 14.0 Tf [(Tuesday, June 28th)] TJ ET
BT 36.266 518.866 Td /F1 12.0 Tf [(9:00am)] TJ ET
BT 84.529 518.261 Td /F2 12.0 Tf [(Richard Bamler - SCGP 102)] TJ ET
BT 84.529 488.890 Td /F2 12.0 Tf [(Speaker: )] TJ ET
BT 133.525 488.890 Td /F1 12.0 Tf [(Richard Bamler )] TJ ET
BT 84.529 460.090 Td /F2 12.0 Tf [(Title: )] TJ ET
BT 115.525 460.090 Td /F1 12.0 Tf [(Towards a theory of Ricci flow in dimension 4 \(and higher\) )] TJ ET
BT 84.529 431.405 Td /F2 12.0 Tf [(Abstract: )] TJ ET
BT 136.177 431.405 Td /F1 12.0 Tf [(The Ricci flow \(with surgery\) has proven to be a powerful tool in the study of 3-)] TJ ET
BT 84.529 417.149 Td /F1 12.0 Tf [(dimensional topology — its most prominent application being the verification of the Poincaré and )] TJ ET
BT 84.529 402.893 Td /F1 12.0 Tf [(Geometrization Conjectures by Perelman about 20 years ago. Since then further research has led to )] TJ ET
BT 84.529 388.637 Td /F1 12.0 Tf [(a satisfactory understanding of the flow and surgery process in dimension 3. In dimensions 4 and )] TJ ET
BT 84.529 374.381 Td /F1 12.0 Tf [(higher, on the other hand, Ricci flows have been understood relatively poorly and a surgery )] TJ ET
BT 84.529 360.125 Td /F1 12.0 Tf [(construction seemed distant. Recently, however, there has been some progress in the form of a new )] TJ ET
BT 84.529 345.869 Td /F1 12.0 Tf [(compactness and partial regularity theory for higher dimensional Ricci flows. This theory relies on )] TJ ET
BT 84.529 331.613 Td /F1 12.0 Tf [(a new geometric perspective on Ricci flows and provides a better understanding of the singularity )] TJ ET
BT 84.529 317.357 Td /F1 12.0 Tf [(formation and long-time behavior of the flow. In dimension 4, in particular, it may eventually open )] TJ ET
BT 84.529 303.101 Td /F1 12.0 Tf [(up the possibility of a surgery construction or a construction of a "flow through singularities". The )] TJ ET
BT 84.529 288.845 Td /F1 12.0 Tf [(goal of this talk will be to describe this new compactness and partial regularity theory and the new )] TJ ET
BT 84.529 274.589 Td /F1 12.0 Tf [(geometric intuition that lies behind it. Next, I will focus on 4-dimensional flows. I will present )] TJ ET
BT 84.529 260.333 Td /F1 12.0 Tf [(applications towards the study of singularities of such flows and discuss several conjectures that )] TJ ET
BT 84.529 246.077 Td /F1 12.0 Tf [(provide a possible picture of a surgery construction in dimension 4. Lastly, I will discuss potential )] TJ ET
BT 84.529 231.706 Td /F1 12.0 Tf [(topological applications. )] TJ ET
BT 36.266 188.626 Td /F1 12.0 Tf [(10:00am)] TJ ET
BT 84.529 188.021 Td /F2 12.0 Tf [(Christos Mantoulidis \(no recording\) - SCGP 102)] TJ ET
BT 84.529 158.650 Td /F2 12.0 Tf [(Speaker: )] TJ ET
BT 133.525 158.650 Td /F1 12.0 Tf [(Christos Mantoulidis )] TJ ET
BT 84.529 129.850 Td /F2 12.0 Tf [(Title: )] TJ ET
BT 115.525 129.850 Td /F1 12.0 Tf [(Decomposing PSC 4-manifolds )] TJ ET
BT 84.529 101.165 Td /F2 12.0 Tf [(Abstract: )] TJ ET
BT 136.177 101.165 Td /F1 12.0 Tf [(We will discuss a decomposition result involving 0- and 1-surgeries for closed, oriented, )] TJ ET
BT 84.529 86.794 Td /F1 12.0 Tf [(topologically PSC 4-manifolds. )] TJ ET
BT 36.266 43.714 Td /F1 12.0 Tf [(11:00am)] TJ ET
BT 84.529 43.109 Td /F2 12.0 Tf [(Coffee Break - SCGP Cafe)] TJ ET
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BT 36.266 744.934 Td /F1 12.0 Tf [(11:30am)] TJ ET
BT 84.529 744.329 Td /F2 12.0 Tf [(Claude LeBrun - SCGP 102)] TJ ET
BT 84.529 714.958 Td /F2 12.0 Tf [(Speaker: )] TJ ET
BT 133.525 714.958 Td /F1 12.0 Tf [(Claude LeBrun )] TJ ET
BT 84.529 686.158 Td /F2 12.0 Tf [(Title: )] TJ ET
BT 115.525 686.158 Td /F1 12.0 Tf [(Kodaira Dimension and the Yamabe Problem, Revisited )] TJ ET
BT 84.529 657.473 Td /F2 12.0 Tf [(Abstract: )] TJ ET
BT 136.177 657.473 Td /F1 12.0 Tf [(Dimension four provides a surprisingly idiosyncratic setting for the interplay between )] TJ ET
BT 84.529 643.217 Td /F1 12.0 Tf [(scalar curvature and differential topology. This peculiarity becomes especially pronounced when )] TJ ET
BT 84.529 628.961 Td /F1 12.0 Tf [(discussing the Yamabe invariant \(or “sigma constant”\) of a smooth compact manifold; and Seiberg-)] TJ ET
BT 84.529 614.705 Td /F1 12.0 Tf [(Witten theory makes this especially apparent for those 4-manifolds that arise as compact complex )] TJ ET
BT 84.529 600.449 Td /F1 12.0 Tf [(surfaces. For compact complex surfaces of Kaehler type, I showed in the late 1990s that the sign of )] TJ ET
BT 84.529 586.193 Td /F1 12.0 Tf [(the Yamabe invariant is always determined by the Kodaira dimension, and moreover calculated the )] TJ ET
BT 84.529 571.937 Td /F1 12.0 Tf [(Yamabe invariant exactly in all cases where it is non-positive. In this talk, I will describe recent )] TJ ET
BT 84.529 557.681 Td /F1 12.0 Tf [(joint work with Michael Albanese that generalizes these results to all complex surfaces of non-)] TJ ET
BT 84.529 543.425 Td /F1 12.0 Tf [(Kaehler type. However, the complex surfaces of class VII actually violate many of the expected )] TJ ET
BT 84.529 529.054 Td /F1 12.0 Tf [(patterns, and navigating around this hazard represents a key aspect of our story. )] TJ ET
BT 36.266 485.974 Td /F1 12.0 Tf [(12:30pm)] TJ ET
BT 84.529 485.369 Td /F2 12.0 Tf [(Lunch - SCGP 102)] TJ ET
BT 36.266 465.718 Td /F1 12.0 Tf [(2:00pm)] TJ ET
BT 84.529 465.113 Td /F2 12.0 Tf [(David Maxwell - SCGP 102)] TJ ET
BT 84.529 435.742 Td /F2 12.0 Tf [(Speaker: )] TJ ET
BT 133.525 435.742 Td /F1 12.0 Tf [(David Maxwell )] TJ ET
BT 84.529 406.942 Td /F2 12.0 Tf [(Title: )] TJ ET
BT 115.525 406.942 Td /F1 12.0 Tf [(Sobolov-Class Asymptotically Hyperbolic Manifolds and the Yamabe Problem )] TJ ET
BT 84.529 378.257 Td /F2 12.0 Tf [(Abstract: )] TJ ET
BT 136.177 378.257 Td /F1 12.0 Tf [(We consider asymptotically hyperbolic manifolds whose metrics have Sobolev-class )] TJ ET
BT 84.529 364.001 Td /F1 12.0 Tf [(regularity. Building on prior work by Allen, Isenberg, Lee, and Allen-Stavrov in the Hölder )] TJ ET
BT 84.529 349.745 Td /F1 12.0 Tf [(category, we introduce two new function spacesfor metrics potentially having a large amount of )] TJ ET
BT 84.529 335.489 Td /F1 12.0 Tf [(interior differentiability measured in Sobolev scales, but whose regularity implies only a Hölder )] TJ ET
BT 84.529 321.233 Td /F1 12.0 Tf [(continuous conformal structure. We establish Fredholm theorems for elliptic operators arising from )] TJ ET
BT 84.529 306.977 Td /F1 12.0 Tf [(metrics in these families.To demonstrate utility of our methods, we solve the Yamabe problem in )] TJ ET
BT 84.529 292.721 Td /F1 12.0 Tf [(this category. As a special limiting case, we show that the asymptotically hyperbolic Yamabe )] TJ ET
BT 84.529 278.465 Td /F1 12.0 Tf [(problem is solvable so long as the metric admits a $W^{1,p}$ conformal compactification, with )] TJ ET
BT 84.529 264.209 Td /F1 12.0 Tf [($p$ greater than the dimension of the manifold.\(Joint with Paul T. Allen, Lewis & Clark and John )] TJ ET
BT 84.529 249.838 Td /F1 12.0 Tf [(M. Lee, University of Washington\) )] TJ ET
BT 36.266 206.758 Td /F1 12.0 Tf [(3:00pm)] TJ ET
BT 84.529 206.153 Td /F2 12.0 Tf [(Jim Isenberg \(remote\) - Zoom)] TJ ET
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BT 84.529 732.214 Td /F2 12.0 Tf [(Speaker: )] TJ ET
BT 133.525 732.214 Td /F1 12.0 Tf [(Jim Isenberg )] TJ ET
BT 84.529 703.529 Td /F2 12.0 Tf [(Title: )] TJ ET
BT 115.525 703.529 Td /F1 12.0 Tf [(Strong Cosmic Censorship and the Stability of AVTD Behavior for Polarized T^2- )] TJ ET
BT 84.529 689.158 Td /F1 12.0 Tf [(Symmetric Space-Times )] TJ ET
BT 84.529 660.473 Td /F2 12.0 Tf [(Abstract: )] TJ ET
BT 136.177 660.473 Td /F1 12.0 Tf [(Penrose’s Strong Cosmic Censorship Conjecture asserts that for generic initial data )] TJ ET
BT 84.529 646.217 Td /F1 12.0 Tf [(satisfying the Einstein constraint equations, the maximal spacetime development of that initial data )] TJ ET
BT 84.529 631.961 Td /F1 12.0 Tf [(cannot be smoothly extended past a Cauchy horizon into a region where determinism breaks down. )] TJ ET
BT 84.529 617.705 Td /F1 12.0 Tf [(This conjecture remains one of the outstanding unresolved issues in mathematical relativity. One of )] TJ ET
BT 84.529 603.449 Td /F1 12.0 Tf [(the most effective tools for proving that Strong Cosmic Censorship holds for a family of )] TJ ET
BT 84.529 589.193 Td /F1 12.0 Tf [(cosmological solutions of Einstein’s equations is to verify that these solutions all exhibit )] TJ ET
BT 84.529 574.937 Td /F1 12.0 Tf [(Asymptotically Velocity Term Dominated \(AVTD\) behavior in a neighborhood of their Big Bang )] TJ ET
BT 84.529 560.681 Td /F1 12.0 Tf [(singularities. After presenting some background history of known results and conjectures )] TJ ET
BT 84.529 546.425 Td /F1 12.0 Tf [(concerning the behavior of the gravitational field near the Big Bang in cosmological solutions of )] TJ ET
BT 84.529 532.169 Td /F1 12.0 Tf [(Einstein’s equations, we discuss recent work with Ellery Ames, Florian Beyer, and Todd Oliynyk )] TJ ET
BT 84.529 517.913 Td /F1 12.0 Tf [(in which we prove that polarized T^2- Symmetric vacuum solutions in a neighborhood of Kasner )] TJ ET
BT 84.529 503.657 Td /F1 12.0 Tf [(solutions all exhibit AVTD behavior close to the initial singularity. We also discuss our very recent )] TJ ET
BT 84.529 489.286 Td /F1 12.0 Tf [(extension of these results to the case of non-vanishing cosmological constant. )] TJ ET
BT 36.266 446.206 Td /F1 12.0 Tf [(4:00pm)] TJ ET
BT 84.529 445.601 Td /F2 12.0 Tf [(Coffee Break - SCGP Cafe)] TJ ET
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BT 258.460 422.695 Td /F2 14.0 Tf [(Wednesday, June 29th)] TJ ET
BT 36.266 404.818 Td /F1 12.0 Tf [(10:00am)] TJ ET
BT 84.529 404.213 Td /F2 12.0 Tf [(Joachim Lohkamp - SCGP 102)] TJ ET
BT 84.529 374.842 Td /F2 12.0 Tf [(Speaker: )] TJ ET
BT 133.525 374.842 Td /F1 12.0 Tf [(Joachim Lohkamp )] TJ ET
BT 84.529 346.042 Td /F2 12.0 Tf [(Title: )] TJ ET
BT 115.525 346.042 Td /F1 12.0 Tf [(Removal of Singularities )] TJ ET
BT 84.529 317.357 Td /F2 12.0 Tf [(Abstract: )] TJ ET
BT 136.177 317.357 Td /F1 12.0 Tf [(Minimal hypersurfaces are important to study general scalar curvatureconstraints. The )] TJ ET
BT 84.529 303.101 Td /F1 12.0 Tf [(occurence of singularitiesis an infamous problem one may solve from an inductive )] TJ ET
BT 84.529 288.845 Td /F1 12.0 Tf [(dimensionalreduction scheme with built-in regularization. We will discuss thisparticular process )] TJ ET
BT 84.529 274.474 Td /F1 12.0 Tf [(and indicated some ways how it can be applied. )] TJ ET
BT 36.266 231.394 Td /F1 12.0 Tf [(11:00am)] TJ ET
BT 84.529 230.789 Td /F2 12.0 Tf [(Coffee Break - SCGP Cafe)] TJ ET
BT 36.266 211.138 Td /F1 12.0 Tf [(11:30am)] TJ ET
BT 84.529 210.533 Td /F2 12.0 Tf [(Dan Lee - SCGP 102)] TJ ET
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BT 84.529 732.214 Td /F2 12.0 Tf [(Speaker: )] TJ ET
BT 133.525 732.214 Td /F1 12.0 Tf [(Dan Lee )] TJ ET
BT 84.529 703.414 Td /F2 12.0 Tf [(Title: )] TJ ET
BT 115.525 703.414 Td /F1 12.0 Tf [(The positive mass theorem with boundaries, complete ends, and scalar curvature shields )] TJ ET
BT 84.529 674.729 Td /F2 12.0 Tf [(Abstract: )] TJ ET
BT 136.177 674.729 Td /F1 12.0 Tf [(In joint work with M. Lesourd and R. Unger, we give a non-spinor proof of the )] TJ ET
BT 84.529 660.473 Td /F1 12.0 Tf [(spacetime positive mass theorem with weakly outer trapped boundary. It turns out that this implies )] TJ ET
BT 84.529 646.217 Td /F1 12.0 Tf [(a version of the Riemannian positive mass theorem that does not require nonnegative scalar )] TJ ET
BT 84.529 631.961 Td /F1 12.0 Tf [(curvature everywhere, so long as the negative scalar curvature is “shielded” from the )] TJ ET
BT 84.529 617.705 Td /F1 12.0 Tf [(asymptotically flat end by a region with sufficiently positive scalar curvature. By an argument of )] TJ ET
BT 84.529 603.449 Td /F1 12.0 Tf [(Lesourd, Unger, and Yau, this latter fact also implies the Riemannian positive mass theorem for )] TJ ET
BT 84.529 589.078 Td /F1 12.0 Tf [(arbitrary complete ends. )] TJ ET
BT 36.266 545.998 Td /F1 12.0 Tf [(12:30pm)] TJ ET
BT 84.529 545.393 Td /F2 12.0 Tf [(Lunch - SCGP Cafe)] TJ ET
BT 36.266 525.742 Td /F1 12.0 Tf [(2:00pm)] TJ ET
BT 84.529 525.137 Td /F2 12.0 Tf [(Pengzi Miao - SCGP 102)] TJ ET
BT 84.529 495.766 Td /F2 12.0 Tf [(Speaker: )] TJ ET
BT 133.525 495.766 Td /F1 12.0 Tf [(Pengzi Miao )] TJ ET
BT 84.529 466.966 Td /F2 12.0 Tf [(Title: )] TJ ET
BT 115.525 466.966 Td /F1 12.0 Tf [(Mass and capacitary potential of asymptotically flat 3-manifolds )] TJ ET
BT 84.529 438.281 Td /F2 12.0 Tf [(Abstract: )] TJ ET
BT 136.177 438.281 Td /F1 12.0 Tf [(I will discuss some relation between the mass and positive harmonic functions decaying )] TJ ET
BT 84.529 423.910 Td /F1 12.0 Tf [(to zero on asymptotically flat 3-manifolds. )] TJ ET
BT 36.266 380.830 Td /F1 12.0 Tf [(3:00pm)] TJ ET
BT 84.529 380.225 Td /F2 12.0 Tf [(David Wiygul - SCGP 102)] TJ ET
BT 84.529 350.854 Td /F2 12.0 Tf [(Speaker: )] TJ ET
BT 133.525 350.854 Td /F1 12.0 Tf [(David Wiygul )] TJ ET
BT 84.529 322.054 Td /F2 12.0 Tf [(Title: )] TJ ET
BT 115.525 322.054 Td /F1 12.0 Tf [(Asymptotic estimates for the Bartnik mass of small metric balls )] TJ ET
BT 84.529 293.369 Td /F2 12.0 Tf [(Abstract: )] TJ ET
BT 136.177 293.369 Td /F1 12.0 Tf [(For all the various definitions of quasilocal mass in general relativity it is natural to )] TJ ET
BT 84.529 279.113 Td /F1 12.0 Tf [(investigate their behavior on regions shrinking to a point. In particular one can seek a Taylor )] TJ ET
BT 84.529 264.857 Td /F1 12.0 Tf [(expansion of the mass of geodesic balls of small radius and fixed center. I will present some recent )] TJ ET
BT 84.529 250.601 Td /F1 12.0 Tf [(estimates for the Bartnik mass in this regime, including one that is obtained by estimating the ADM )] TJ ET
BT 84.529 236.345 Td /F1 12.0 Tf [(mass of asymptotically flat static vacuum extensions with "small" Bartnik boundary data to second )] TJ ET
BT 84.529 221.974 Td /F1 12.0 Tf [(order in the data. )] TJ ET
BT 36.266 178.894 Td /F1 12.0 Tf [(4:00pm)] TJ ET
BT 84.529 178.289 Td /F2 12.0 Tf [(Coffee Break - SCGP Cafe)] TJ ET
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BT 263.899 155.383 Td /F2 14.0 Tf [(Thursday, June 30th)] TJ ET
BT 36.266 137.506 Td /F1 12.0 Tf [(9:00am)] TJ ET
BT 84.529 136.901 Td /F2 12.0 Tf [(Bernhard Hanke - SCGP 102)] TJ ET
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BT 84.529 732.214 Td /F2 12.0 Tf [(Speaker: )] TJ ET
BT 133.525 732.214 Td /F1 12.0 Tf [(Bernhard Hanke)] TJ ET
BT 84.529 689.014 Td /F2 12.0 Tf [(Title: )] TJ ET
BT 115.525 689.014 Td /F1 12.0 Tf [(Lipschitz rigidity for scalar curvature)] TJ ET
BT 84.529 645.929 Td /F2 12.0 Tf [(Abstract: )] TJ ET
BT 136.177 645.929 Td /F1 12.0 Tf [(Let M be a closed connected smooth spin manifold of even dimension n, let g be a )] TJ ET
BT 84.529 631.673 Td /F1 12.0 Tf [(Riemannian metric of regularity W^{1,p}, p > n, on M whose distributional scalar curvature in the )] TJ ET
BT 84.529 617.417 Td /F1 12.0 Tf [(sense of Lee-LeFloch is bounded below by n\(n-1\), and let f : \(M,g\) \\to S^n be a 1-Lipschitz )] TJ ET
BT 84.529 603.046 Td /F1 12.0 Tf [(continuous map of non-zero degree to the standard round n-sphere. )] TJ ET
BT 84.529 588.761 Td /F1 12.0 Tf [(Then f is a metric isometry. This generalizes a result of Llarull \(1998\) and answers a question of )] TJ ET
BT 84.529 574.505 Td /F1 12.0 Tf [(Gromov \(2019\) in his ``four lectures’’. Our proof, which is a joint work with Simone Cecchini and )] TJ ET
BT 84.529 560.249 Td /F1 12.0 Tf [(Thomas Schick, combines spectral properties of Dirac operators for metrics with low regularity and )] TJ ET
BT 84.529 545.878 Td /F1 12.0 Tf [(twisted with Lipschitz bundles with the theory of quasiregular maps due to Reshetnyak. )] TJ ET
BT 36.266 488.398 Td /F1 12.0 Tf [(10:00am)] TJ ET
BT 84.529 487.793 Td /F2 12.0 Tf [(Guoliang Yu - SCGP 102)] TJ ET
BT 84.529 458.422 Td /F2 12.0 Tf [(Speaker: )] TJ ET
BT 133.525 458.422 Td /F1 12.0 Tf [(Guoliang Yu )] TJ ET
BT 84.529 429.622 Td /F2 12.0 Tf [(Title: )] TJ ET
BT 115.525 429.622 Td /F1 12.0 Tf [(Higher index theory and scalar curvature )] TJ ET
BT 84.529 400.937 Td /F2 12.0 Tf [(Abstract: )] TJ ET
BT 136.177 400.937 Td /F1 12.0 Tf [(I will give an introduction to higher index theory of Dirac operators and its applications )] TJ ET
BT 84.529 386.681 Td /F1 12.0 Tf [(to scalar curvature.In particular, I will discuss my recent joint work with Shmuel Weinberger and )] TJ ET
BT 84.529 372.425 Td /F1 12.0 Tf [(Zhizhang Xie on higher index theory at infinityand its applications to Gromov's compactness )] TJ ET
BT 84.529 358.054 Td /F1 12.0 Tf [(conjecture on scalar curvature. )] TJ ET
BT 36.266 314.974 Td /F1 12.0 Tf [(11:00am)] TJ ET
BT 84.529 314.369 Td /F2 12.0 Tf [(Coffee Break - SCGP Cafe)] TJ ET
BT 36.266 294.718 Td /F1 12.0 Tf [(11:30am)] TJ ET
BT 84.529 294.113 Td /F2 12.0 Tf [(Demetre Kazaras - SCGP 102)] TJ ET
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BT 84.529 732.214 Td /F2 12.0 Tf [(Speaker: )] TJ ET
BT 133.525 732.214 Td /F1 12.0 Tf [(Demetre Kazaras)] TJ ET
BT 84.529 689.014 Td /F2 12.0 Tf [(Title: )] TJ ET
BT 115.525 689.014 Td /F1 12.0 Tf [(Comparison geometry and spacetime harmonic functions)] TJ ET
BT 84.529 645.929 Td /F2 12.0 Tf [(Abstract: )] TJ ET
BT 136.177 645.929 Td /F1 12.0 Tf [(Comparison theorems are the basis for our geometric understanding of Riemannian )] TJ ET
BT 84.529 631.673 Td /F1 12.0 Tf [(manifolds satisfying a given curvature condition. A remarkable example is the Gromov-Lawson )] TJ ET
BT 84.529 617.417 Td /F1 12.0 Tf [(toric band inequality, which bounds the distance between the two sides of a Riemannian torus-)] TJ ET
BT 84.529 603.161 Td /F1 12.0 Tf [(cross-interval with positive scalar curvature by a sharp constant inversely proportional to the scalar )] TJ ET
BT 84.529 588.905 Td /F1 12.0 Tf [(curvature's minimum. We will give a new qualitative version of this and similar band-type )] TJ ET
BT 84.529 574.649 Td /F1 12.0 Tf [(inequalities in dimension 3 using the notion of spacetime harmonic functions, which recently )] TJ ET
BT 84.529 560.393 Td /F1 12.0 Tf [(played the lead role in our recent proof of the positive mass theorem. Other applications include )] TJ ET
BT 84.529 546.137 Td /F1 12.0 Tf [(new versions of Bonnet-Meyer's diameter estimate for positive Ricci curvature manifolds and )] TJ ET
BT 84.529 531.881 Td /F1 12.0 Tf [(Llarull's theorem which do not require a completeness assumption. This is joint work with Sven )] TJ ET
BT 84.529 517.510 Td /F1 12.0 Tf [(Hirsch, Marcus Khuri, and Yiyue Zhang.)] TJ ET
BT 36.266 460.030 Td /F1 12.0 Tf [(12:30pm)] TJ ET
BT 84.529 459.425 Td /F2 12.0 Tf [(Lunch - SCGP Cafe)] TJ ET
BT 36.266 439.774 Td /F1 12.0 Tf [(2:00pm)] TJ ET
BT 84.529 439.169 Td /F2 12.0 Tf [(Rudolf Zeidler - SCGP 102)] TJ ET
BT 84.529 409.798 Td /F2 12.0 Tf [(Speaker: )] TJ ET
BT 133.525 409.798 Td /F1 12.0 Tf [(Rudolf Zeidler )] TJ ET
BT 84.529 380.998 Td /F2 12.0 Tf [(Title: )] TJ ET
BT 115.525 380.998 Td /F1 12.0 Tf [(Distance estimates under lower scalar curvature bounds in the spin setting and beyond )] TJ ET
BT 84.529 352.313 Td /F2 12.0 Tf [(Abstract: )] TJ ET
BT 136.177 352.313 Td /F1 12.0 Tf [(We will discuss several situations in which lower scalar curvature bounds can be used to )] TJ ET
BT 84.529 338.057 Td /F1 12.0 Tf [(infer certain distance estimates using the Dirac operator on spin manifolds. This includes Gromov’s )] TJ ET
BT 84.529 323.801 Td /F1 12.0 Tf [(question on the distance between the boundary components of „bands“, rigidity properties of )] TJ ET
BT 84.529 309.545 Td /F1 12.0 Tf [(warped products, and related questions in the context of Witten’s spinor proof of the positive mass )] TJ ET
BT 84.529 295.289 Td /F1 12.0 Tf [(theorem. Finally, we will contrast this with a recently obtained result in the non-spin setting )] TJ ET
BT 84.529 281.033 Td /F1 12.0 Tf [(concerning the non-existence of complete psc metrics on certain manifolds which admit a compact )] TJ ET
BT 84.529 266.662 Td /F1 12.0 Tf [(incompressible hypersurface without psc. Based on joint works with S. Cecchini and D. Räde. )] TJ ET
BT 36.266 223.582 Td /F1 12.0 Tf [(3:00pm)] TJ ET
BT 84.529 222.977 Td /F2 12.0 Tf [(Daniel Räde - SCGP 102)] TJ ET
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BT 84.529 732.214 Td /F2 12.0 Tf [(Speaker: )] TJ ET
BT 133.525 732.214 Td /F1 12.0 Tf [(Daniel Räde)] TJ ET
BT 84.529 689.014 Td /F2 12.0 Tf [(Title: )] TJ ET
BT 115.525 689.014 Td /F1 12.0 Tf [(Scalar and mean curvature comparison for Riemannian bands)] TJ ET
BT 84.529 645.929 Td /F2 12.0 Tf [(Abstract: )] TJ ET
BT 136.177 645.929 Td /F1 12.0 Tf [(We use $\\mu$-bubbles to compare Riemannian bands in scalarcurvature, mean )] TJ ET
BT 84.529 631.673 Td /F1 12.0 Tf [(curvature and width to warped products over scalar flatmanifolds with $\\log$-concave warping )] TJ ET
BT 84.529 617.417 Td /F1 12.0 Tf [(functions. Furthermore we explainhow these comparison results can be used to prove two )] TJ ET
BT 84.529 603.161 Td /F1 12.0 Tf [(conjectures due toGromov resp. Rosenberg and Stolz in dimensions $\\leq 7$. Thistalk is, in part, )] TJ ET
BT 84.529 588.790 Td /F1 12.0 Tf [(based on joint work with S. Cecchini and R. Zeidler.)] TJ ET
BT 36.266 531.310 Td /F1 12.0 Tf [(4:00pm)] TJ ET
BT 84.529 530.705 Td /F2 12.0 Tf [(Coffee Break - SCGP Cafe)] TJ ET
BT 36.266 511.054 Td /F1 12.0 Tf [(6:00pm)] TJ ET
BT 84.529 510.449 Td /F2 12.0 Tf [(Banquet - SCGP Cafe)] TJ ET
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BT 279.075 487.543 Td /F2 14.0 Tf [(Friday, July 1st)] TJ ET
BT 36.266 469.666 Td /F1 12.0 Tf [(10:00am)] TJ ET
BT 84.529 469.061 Td /F2 12.0 Tf [(Carla Cederbaum - Zoom)] TJ ET
BT 84.529 439.690 Td /F2 12.0 Tf [(Speaker: )] TJ ET
BT 133.525 439.690 Td /F1 12.0 Tf [(Carla Cederbaum )] TJ ET
BT 84.529 410.890 Td /F2 12.0 Tf [(Title: )] TJ ET
BT 115.525 410.890 Td /F1 12.0 Tf [(Coordinates are messy )] TJ ET
BT 84.529 382.205 Td /F2 12.0 Tf [(Abstract: )] TJ ET
BT 136.177 382.205 Td /F1 12.0 Tf [(Asymptotically Euclidean initial data sets $\(M,g,K\)$ are characterized by the existence )] TJ ET
BT 84.529 367.949 Td /F1 12.0 Tf [(of asymptotic coordinates in which the Riemannian metric $g$ and second fundamental form $K$ )] TJ ET
BT 84.529 353.693 Td /F1 12.0 Tf [(decay to the Euclidean metric $\\delta$ and to $0$ suitably fast, respectively. Provided their matter )] TJ ET
BT 84.529 339.437 Td /F1 12.0 Tf [(densities satisfy suitable integrability conditions, they have well-defined \(ADM-\)energy, \(ADM-)] TJ ET
BT 84.529 325.181 Td /F1 12.0 Tf [(\)linear momentum, and \(ADM-\)mass as was shown by Bartnik in 1986. To study their \(ADM-)] TJ ET
BT 84.529 310.925 Td /F1 12.0 Tf [(\)angular momentum and \(BORT-\)center of mass, one usually assumes the existence of so-called )] TJ ET
BT 84.529 296.669 Td /F1 12.0 Tf [(Regge—Teitelboim coordinates. We will give examples of asymptotically Euclidean initial data )] TJ ET
BT 84.529 282.413 Td /F1 12.0 Tf [(sets which do not possess any Regge—Teitelboim coordinates and explain other “non-features” of )] TJ ET
BT 84.529 268.157 Td /F1 12.0 Tf [(the Regge—Teitelboim coordinate conditions. This is joint work with Melanie Graf and Jan )] TJ ET
BT 84.529 253.901 Td /F1 12.0 Tf [(Metzger. We will also explain the consequences of these findings for the definition of the center of )] TJ ET
BT 84.529 239.530 Td /F1 12.0 Tf [(mass, relying on joint work with Nerz and with Sakovich. )] TJ ET
BT 36.266 196.450 Td /F1 12.0 Tf [(11:00am)] TJ ET
BT 84.529 195.845 Td /F2 12.0 Tf [(Coffee Break - SCGP Cafe)] TJ ET
BT 36.266 176.194 Td /F1 12.0 Tf [(11:30am)] TJ ET
BT 84.529 175.589 Td /F2 12.0 Tf [(Zhongshan An - SCGP 102)] TJ ET
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BT 84.529 732.214 Td /F2 12.0 Tf [(Speaker: )] TJ ET
BT 133.525 732.214 Td /F1 12.0 Tf [(Zhongshan An )] TJ ET
BT 84.529 703.414 Td /F2 12.0 Tf [(Title: )] TJ ET
BT 115.525 703.414 Td /F1 12.0 Tf [(Local existence and uniqueness of static vacuum extensions of Bartnik boundary data )] TJ ET
BT 84.529 674.729 Td /F2 12.0 Tf [(Abstract: )] TJ ET
BT 136.177 674.729 Td /F1 12.0 Tf [(The study of static vacuum Riemannian metrics arises naturally in differential geometry )] TJ ET
BT 84.529 660.473 Td /F1 12.0 Tf [(and general relativity. It plays an important role in scalar curvature deformation, as well as )] TJ ET
BT 84.529 646.217 Td /F1 12.0 Tf [(constructing Einstein spacetimes. Existence of static vacuum Riemannian metrics with prescribed )] TJ ET
BT 84.529 631.961 Td /F1 12.0 Tf [(Bartnik data — the induced metric and mean curvature of the boundary — is one of the most )] TJ ET
BT 84.529 617.705 Td /F1 12.0 Tf [(fundamental problems in Riemannian geometry related to general relativity. It is also a very )] TJ ET
BT 84.529 603.449 Td /F1 12.0 Tf [(interesting problem on the global solvability of a natural geometric boundary value problem. In this )] TJ ET
BT 84.529 589.193 Td /F1 12.0 Tf [(talk I will first discuss some basic properties of the nonlinear and linearized static vacuum )] TJ ET
BT 84.529 574.937 Td /F1 12.0 Tf [(equations and the geometric boundary conditions. Then I will present some recent progress towards )] TJ ET
BT 84.529 560.566 Td /F1 12.0 Tf [(the existence problem of static vacuum metrics based on joint works with Lan-Hsuan Huang. )] TJ ET
BT 36.266 517.486 Td /F1 12.0 Tf [(12:30pm)] TJ ET
BT 84.529 516.881 Td /F2 12.0 Tf [(Lunch - SCGP Cafe)] TJ ET
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