I will discuss the picture for quartic K3 surfaces, relating compactifications coming from geometric invariant theory (GIT), Hodge theory, and K-stability via wall crossings in K-moduli. The stable degeneration conjecture, due to Li and Xu, predicts a local stability theory of klt singularities through the minimizers of the the normalized volume functions. Over non-closed fields, BenoistWittenberg, formalizing earlier observations of HassettTschinkel, defined certain torsors over the intermediate Jacobian and showed that they carry further obstructions to rationality. In 1993, Morrison conjectured that the automorphism group of a Calabi-Yau 3-fold acts on its nef cone with a rational polyhedral fundamental domain. Abstract: In this talk we propose a connection between Zamolodshikov's c type theorems and upersemicontinuity of spectra. A big open problem surrounding hyperkhler manifolds is the construction of new examples: currently there are only 4 known deformation types. in order for the action functional of higher abelian Chern-Simons theory to be correctly divisible, the images of the fields in 2 \mathbb{Z}_2-cohomology need to form a twisted Wu structure. For driving directions to Danfords Hotel & Marina, please click here. ALL in-person meeting attendees must be vaccinated against the COVID-19 virus with a World Health Organization approved vaccine, be beyond the 14-day inoculation period of their final dose, and provide proof of vaccination upon arrival to the conference. Giulio Codogni Chi Li Erik Paemurru Travel to the Port Jefferson Station Non-Archimedean functionals and K-stability for log Fano cones. This is based on joint work with Harold Blum and Yuchen Liu. K-stability of moduli of bundles on curves. Mori conjectured that this is true when d is prime and n>2 (it is not difficult to produce limits that are not hypersurfaces when d is composite). For more information please visithttps://sites.google.com/view/simonsconfe rences/. The local-global analogy between klt singularities and Fano varieties, together with recent study in K-stability lead to the conjecture that klt singularities whose local volumes are bounded away from zero are bounded up to special degeneration. Actually, it seems that Bir(X) is most of time either finite or not simple, if X is an algebraic variety. While the theories of KSBA-stability and K-stability have been successful in constructing compact moduli spaces of canonically polarized varieties and Fano varieties, respectively, the case of K-trivial varieties remains less well understood. eklein@simonsfoundation.org, Subscribe to MPS announcements and other foundation updates, We use cookies to analyze web traffic and to improve your browsing experience; full details are in our, can be found at the bottom of this page on the WHOs site. Roberto Svaldi, EPFL Mori's Conjecture, Plane Curves, and Markov Numbers. > math > arXiv:2211.02290 . On the rationality of Fano-Enriques threefolds with terminal cyclic quotient singularities. By clicking to watch this video, you agree to our privacy policy. From NYC Penn Station: The local-global analogy between klt singularities and Fano varieties, together with recent study in K-stability lead to the conjecture that klt singularities whose local volumes are bounded away from zero are bounded up to special degeneration. To such non-taut RDPs Artin assigned a coindex distinguishing the ones with the same resolution graph in terms of their deformation theory. Ziquan Zhuang - Boundedness of singularities and minimal log discrepancies of Kollr components. David Stapleton - Mori's Conjecture, Plane Curves, and Markov Numbers. In this talk, we will consider singular del Pezzo surfaces which are quasi-smooth, well-formed hypersurfaces in weighted projective space, and understand what we can say about their K-stability. If time permits, I will also discuss several applications of our result, e.g. Susanna Zimmermann - Algebraic groups acting birationnally on the plane over a non-closed field. The talk is based on a joint work and a work in progress with L. Tasin and F. Viviani. Chenyang Xu Ivan Cheltsov, University of Edinburgh Wednesday February 23 to Friday February 25 2022. In this talk, I will explain how to answer the question Which rational double points (and configurations of them) occur on del Pezzo surfaces? for all RDP del Pezzo surfaces in all characteristics. Speaker: Alexandr Andoni, Microsoft Research For many computational problems, it is beneficial to see them through the prism of high-dimensional geometry. Abstract: Fix a degree d and a dimension n. When is every smooth projective limit of degree d and dimension n hypersurfaces a hypersurface? Stable degenerations of klt singularities. For those flying into LGA you will have to catch the Long Island Railroad at Jamaica Station in Queens. Should you have any questions, please contact Emily Klein. University of Utah College of Science 1430 Presidents Circle, Room 220 Salt Lake City, Utah 84112-0140 (801) 581-6958 fax: (801) 585-3169 This is joint work with Kenny Ascher, Giovanni Inchiostro, and Zsolt Patakfalvi. I will also discuss some examples and applications. In this talk, I will describe the compactification of the family of Fano threefolds, which is obtained by blowing up the projective space along a complete intersection of two quadrics which is an elliptic curve, into a K-moduli space using Geometric Invariant Theory (GIT). Please provide your travel specifications by clicking the registration link above. These have been classified in 1, 10 and 105 families in dimensions 1, 2 and 3 respectively, while in higher dimensions the number of Fano families is yet unknown. This is the form of the action functional first given as (Witten96 (3.6)) in for the case k = 1 k = 1.In the language of twisted differential c-structures, we may summarize this sitation as follows:. Jakob Witaszek, University of Michigan We also propose an approach to studying this problem using Hacking's work on the KSBA compactification of the moduli space of plane curve pairs. on quotients of Fano type varieties, good moduli spaces, and collapsing of homogeneous bundles. Zamolodchikovs c theorems and nonrationality. Algebraic groups acting birationally on the plane over a non-closed field. In higher dimension, there are partial classifications in dimension 3. Mircea Musta, University of Michigan Any additional nights are at the attendees own expense. A conifold transition first contracts X along disjoint rational curves with normal bundles of type (-1,-1), and then smooths the resulting singular complex space Z to a new compact complex manifold Y. Simons Foundation: Higher Dimensional Geometry: August 22 - 26, 2022 . Meeting Goals: The MPS Conference on Higher Dimensional Geometry, February 2022 focused on recent progress in higher-dimensional geometry and its interaction with other fields. Abstract: The intermediate Jacobian is an obstruction to rationality in dimension 3, first introduced over the complex numbers by ClemensGriffiths in their proof of the irrationality of the cubic threefold. > hep-th > arXiv:hep-th/9810135 . A conifold transition is a geometric transformation that is used to connect different moduli spaces of Calabi-Yau threefolds. In this talk, I will survey the local stability theory. Such Y is called a Clemens manifold and can be non-Kahler. Why make your job harder? Chenyang Xu, Princeton University It is sometimes referred to as "Higher Elevation Smoke Shop & Gallery". A cone conjecture for log Calabi-Yau surfaces. Nikita Nekrasov Awarded 2023 Dannie Heineman Prize for Mathematical Physics, Avia Raviv-Moshe Awarded the 2022 Womens Postdoctoral Career Development Award in Science, Professor Zohar Komargodski Awarded the Tomassoni Chisesi Prize, SCGP COVID Protocols for Program Visitors and Workshop Participants, COVID-19: Advisory and Updates March 2022, https://www.simonsfoundation.org/event/mps-conference-on-higher-dimensional-geometry-august-22-26-2022/, Simons Foundation Conference on Higher Dimensional Geometry: May 8 12, 2023, C.N. You can take public transportation to Jamaica via the Q33 bus and then the E train; however, taking a taxi may be more convenient. Reductive quotients of klt varieties. In addition, the automorphism group of the unique surface with a split mixed Hodge structure in each deformation type acts on the nef effective cone with a rational polyhedral fundamental domain. Claudia Stadlmayr Additional information in this regard will be emailed on the final day of the meeting. An important category of geometric objects in algebraic geometry is smooth Fano varieties. We discuss how to find all K-polystable smooth Fano threefolds that can be obtained as blowup of P^3 along the disjoint union of a twisted cubic curve and a line. Kristin DeVleming, University of Massachusetts Participation in the meeting falls into the following three categories. Business-class or premium economy airfare will be booked for all flights over five hours. K-stability was introduced by Tian and Donaldson to characterize the solution of the Kahler-Einstein problem on Fano varieties. Dori Bejleri, Harvard University Topics included K-stability and recent progress on the construction of the moduli space of K-stable Fano varieties, the minimal model program in mixed characteristic and the higher dimensional Cremona group. Take the AirTrain JFK towards Jamaica For del Pezzo surfaces with quotient singularities, there are partial results. Once at Penn Station, board a Port Jefferson- bound Long Island Rail Road train. In the past few years, a lot of interests were attracted to the Stable Degeneration Conjecture, and it was completely settled recently (for the last step, see Ziquan Zhuangs lecture in this conference). Simons Foundation Conference on Higher Dimensional Geometry: May 8 - 12, 2023. Yuchen Liu (3 lectures) As main application, I will give a quantitative description of a portion of the ample cone of KSB moduli spaces. Abstract: The group of birational transformations of the projective space has been recently proven to be not simple in any dimension at least 2. Minimal model program for foliated surfaces: a different approach. The proof uses the theory of limiting mixed Hodge structures and basic linear algebra. Simons Collaboration on Global Categorical Symmetries . Abstract: Stable log varieties or stable pairs (X,D) are the higher dimensional generalization of pointed stable curves. NASA ADS; Bookmark (what is this?) Looking to be added to our talks list? Mathematics > Differential Geometry. An important category of geometric objects in algebraic geometry is smooth Fano varieties. Rationality of conic bundle threefolds over non-closed fields. Group C Local Participants Kristin DeVleming - K stability and birational geometry of moduli spaces of quartic K3 surfaces. These stable pair compactifications depend on a choice of parameters, namely the coefficients of the boundary divisor D. In this talk, after introducing the theory of stable log varieties, I will explain the wall-crossing behavior that governs how these compactifications change as one varies the coefficients. I will describe the cases of conic bundles, del Pezzo fibrations and surfaces. Simons Foundation: Higher Dimensional Geometry: 2022-09-11: 2022-09-14: Simons Collaboration on Special Holonomy in Geometry, Analysis, and Physics: Progress and Open Problems: . They form proper moduli spaces which compactify the moduli space of normal crossings, or more generally klt, pairs. the Simons Foundation and member institutions. For example, one can . This is joint work with K. Ascher, D. Bejleri, K. DeVleming, G. Inchiostro, Y. Liu, X. Wang. Paolo Cascini, Ivan Cheltsov, James McKernan and Chenyang Xu. I will conclude by explaining some important applications of these types of singularities to degenerations and deformations of algebraic varieties. For example, Griffin showed there is a family of smooth quintic curves with a smooth limit that is not a plane curve. A more interesting setting occurs in the case of pairs of varieties and a hyperplane section where the K-moduli compactifications tessellate depending on a parameter. We prove that any small smoothing Y of Z satisfies ddbar-lemma. An important problem is compactifying these families into moduli spaces via K-stability. Ziquan Zhuang Survey of local stability theory. Yueqiao Wu . SCGP has a gated parking lot. The idea of a higher-dimensional space was expressed by I. Kant (1746), while J. d'Alembert (1764) wrote on attaching to space the time as a fourth coordinate. The city at the geographic halfway point from Bend, OR to Portola, CA is Grizzlie Place, California. What we do, and what we are all about? This is joint work in preparation with Kristin DeVleming. Jakub Witaszek - Classification of algebraic varieties in positive and mixed characteristic. Abstract: There are many algebraic groups acting birationnally on a projective space, and for the complex plane have been mostly classified. Boundedness of singularities and minimal log discrepancies of Kollr components. Want to know what is happening at the Center? Lecture 1: Algorithmic High-Dimensional Geometry I Lecture 2: Algorithmic High-Dimensional Geometry II This series of talks was part of the Big Data Boot Camp. 1. Acceptable vaccines can be found at the bottom of this page on the WHOs site. Boston, MA. Elena Denisova In this talk I will motivate the classification for infinite algebraic groups acting on the plane over a perfect field. The intermediate Jacobian is an obstruction to rationality in dimension 3, first introduced over the complex numbers by ClemensGriffiths in their proof of the irrationality of the cubic threefold. Organizer: Robert Bryant. The price to pay for working with these divisors is to define a new category of singularities for foliated varieties. Abstract: Stable log varieties or stable pairs (X,D) are the higher dimensional generalization of pointed stable curves. Calum Spicer, Kings College London Moduli of varieties of general type. Participants in Groups A & B who require accommodations are hosted by the foundation for a maximum of six nights at Danfords Hotel & Marina (check in August 21; check out August 27). 4. Hermann Grassmann in Germany was one of the first to develop a full geometry that worked in dimensions higher than three, and . Lisa Marquand Take the Air Train to the New Jersey Transit and then take the New Jersey Transit to NYC Penn Station. In the literature, local analytic types of 3-dimensional divisorial contractions with centre a point have been almost classified. In this talk, I will explain the proof of the recent result, obtained together with Daniel Greb, Kevin Langlois, and Joaquin Moraga,that reductive quotients of klt type varieties are of klt type. As a corollary, we show that the set of rationally connected threefold \(X\) which has an \((\epsilon,\mathbb{R}r)\)-complement is bounded in codimension one. Participants may drive to and from SCGP (a 15-minute drive) or take the shuttle bus. Simons Foundation: Higher Dimensional Geometry: August 22 - 26, 2022 Generalized Global Symmetries, Quantum Field Theory, and Geometry: September 19-23, 2022 Mailing List Lu Qi We discuss the moduli theory of varieties of general type, focusing on new results and open problems. Exit at Port Jefferson Station. Abstract: Recently it has been shown that K-stability provides well-behaved moduli spaces of Fano varieties and log Fano pairs, and allows one to naturally interpolate between other geometric compactifications. This is joint work with Kenneth Ascher and Yuchen Liu. Lena Ji, University of Michigan Stable log varieties or stable pairs (X,D) are the higher dimensional generalization of pointed stable curves. It was perfectly possible to have a higher-dimensional geometry satisfying axioms that were exactly analogous to all the axioms of Euclid, so that any triangle would have its angle sum precisely equal to 180 degrees. Here is where you do just that. An individuals participation category is communicated via their letter of invitation. These stable pair compactifications depend on a choice of parameters, namely the coefficients of the boundary divisor D. In this talk, after introducing the theory of stable log varieties, I will explain the wall-crossing behavior that governs how these compactifications change as one varies the coefficients. . Recently, M. Musta, M. Popa, M. Saito and their collaborators have introduced a natural generalization of the Du Bois singularities, the higher Du Bois singularities. The initial doubts and mysticism associated with the . 2022. 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