Frank calegari. Relation with special values of periods 3 3.
Frank calegari arXiv; On the multiplicity of linear recurrence sequences. From: Frank Calegari Tue, 25 Dec 2018 00:22:23 UTC (166 KB) [v2] Thu, 16 Jun 2022 17:57:08 UTC (186 KB) Full-text links: Access Paper: View a PDF of the paper titled Potential automorphy over CM fields, by Patrick B. The Mahler lectures are a biennial activity organised by the Australian Mathematical Society, and supported by the Australian Mathematical Frank Calegari, Søren Galatius, Akshay Venkatesh, Arbeitsgemeinschaft: Derived Galois Deformation Rings and Cohomology of Arithmetic Groups. The tour 2 FRANK CALEGARI the space constraints and the competence of the author. 9, 1893-1907. As a consequence, we obtain the expected meromorphic continuation and functional equations of their Hasse--Weil zeta functions. Patching and the p-adic local Langlands correspondence (with Ana Caraiani, Toby Gee, David Geraghty, Vytas Paskunas, and Sug Woo Shin) Again we remark that the values Z 2,2,1 (2, 1/2) and Z 2,2,1 (3, 1/2) were shown to be irrational by Calegari [2], by comparison with (4. The University of Chicago Department of Mathematics. Let F/Q be an imaginary quadratic field, and let p > 2 be a prime which is unramified in F. under a certain local non-vanishing assumption we prove the rationality Instructor: Frank Calegari Time and place: MWF 11:00 a. Thorne Authors: George Boxer, Frank Calegari, Toby Gee, Vincent Pilloni. Allen and 9 other authors. 1, 91–108 DOI: 10. His research focuses on the Langlands programme, Galois representations, motives, and automorphic forms. Danny Matthew Cornelius Calegari is a mathematician and, as of 2023, a professor of mathematics at the University of Chicago. Even with the absence of any real mathematical details in this paper, the sheer amount of activity in this eld has led me to discard any discussion of advances not directly related to R= T theorems, which necessitates the omission of a lot of closely related beautiful View a PDF of the paper titled The Unbounded Denominators Conjecture, by Frank Calegari and Vesselin Dimitrov and Yunqing Tang. Tiep) The adelic closure of triangle groups Frank Calegari is an associate chair and a professor of mathematics at the University of Chicago. From: Frank Calegari [v1] Mon, 29 Jul 2024 18:54:06 UTC (21 KB) Full-text links: Access Paper: View a PDF of the paper titled The adelic closure of triangle groups, by Frank Calegari. In this paper, we study the nearly ordinary deformations of ρ. Galois images of Picard curves, with Frank Calegari. Dates Published 25 August 2022 Identifiers DOI 10. TANG 7. This conference will mark the centennial of his birth with lectures related to his work and recollections from colleagues, family and friends. To submit students of this mathematician, please use the new data form, noting this mathematician's MGP ID of 59351 for the advisor ID. AU - Handfield, Toby. This representation corresponds to a tessellation of the upper half plane H by hyperbolic triangles with angles π/p, π/q, and π/r. Class time: MWF, 11:00–12:00. Search 211,385,908 papers from all fields of science. Noah Caplinger Graduate Student Kapil Chandran. This is the “endowment effect”, which has been widely documented in human populations and also in some non-human species. Math 153 (2017), no. Mingjia Zhang 张明嘉 - Moduli Stacks of 𝘱-adic Shtukas and Integral Models of Sh. Bloch groups, algebraic K-theory, units, and Nahm’s conjecture. group can be considered as an elliptic analogue of the class group, one might expect in analogy with genus theory to find that mE satisfies certain divisibility properties, especially, perhaps, by FRANK CALEGARI 1. This is in accordance with the Fontaine–Mazur conjecture. (I also used this as the site for 25700/25800/5900 when I taught online in 2020, thus the URL. Previous generalizations of these methods have been restricted to situations where the automorphic forms in question contribute to a single degree of cohomology. Coherent Cohomology 6 4. This Year's AWS: This Year's PAWS: Last Year's Winter School: Index of Winter Schools Special public lecture: How to solve equations in rational numbers Professor Frank Calegari. Dolfi, G. Motivated by questions arising from billiard trajectories in the regular n-gon, Mc-Mullen [McM24] defined a pair of functions κ and δ on the cusps c of the corresponding triangle group ∆n inside SL2(O), where O = Z[ζn + ζ −1 n]. I used to maintain links to friends and collaborators (and my brother Danny) but collaborators are now linked on my research page and I didn't maintain these links anyway. GEORGE BOXER, FRANK CALEGARI, TOBY GEE, AND VINCENT PILLONI Abstract. We prove new modularity lifting theorems for p-adic Galois representations in situations where the methods of Wiles and Taylor–Wiles do not apply. 16100 course web page; View a PDF of the paper titled Irrationality of certain p-adic periods for small p, by Frank Calegari. Introduction 1 1. View PDF; TeX Source; Other let $\pi$ be a cuspidal automorphic representation of $\mathrm{gl}_n(\mathbb{a}_{\mathbb{q}})$ with non-vanishing cohomology. The geometry of E is at present poorly understood, and seems quite complicated, especially over the centre of weight space. Download PDF Abstract: The modular degree m_E of an elliptic curve E/Q is the minimal degree of any surjective morphism X_0(N) -> E, where N is the conductor of E. Frank Calegari grew up in Melbourne, and was one of Australia's representatives in the International Mathematical Olympiad in 1992 and 1993. 1001–1046. Australian mathematician. Approximations of real numbers A criteria for irrationality Rational numbers are poorly approximated by rational numbers different from themselves. Jayne Ion. Geraghty; Published 27 September 2012; Mathematics; arXiv: Number Theory; In a previous paper [CG], we showed how one could generalize Taylor-Wiles modularity lifting theorems [Wil95, TW95] to contexts beyond those in which the automorphic forms in question arose from the middle degree cohomology of Shimura Kevin Buzzard∗ Frank Calegari† July 5, 2005 1 Introduction In [7], Coleman and Mazur construct a rigid analytic space E that parameterizes overcon-vergent and therefore classical modular eigenforms of finite slope. Our results apply to Galois repre-sentations over Q with image S 5 satisfying certain local hypotheses, the most important of which is Friends of Frank Calegari. View a PDF of the paper titled Bloch groups, algebraic K-theory, units, and Nahm's Conjecture, by Frank Calegari and Stavros Garoufalidis and Don Zagier. 2 Corpus ID: 119605045; Potential automorphy over CM fields @article{Allen2018PotentialAO, title={Potential automorphy over CM fields}, author={Patrick Brodie Allen and Frank Calegari and Ana Caraiani and Toby Gee and David Helm and Bao Viet Le Hung and James Newton and Peter Scholze and Richard Taylor and Jack A. Acknowledgements 3 2. Frank Calegari The University of Chicago, 5734 S University Ave, Chicago, IL 60637, USA; Download Chapter PDF. Sign In The first results towards 1. 25). p-adic modular forms 20 2. View a PDF of the paper titled A torsion Jacquet--Langlands correspondence, by Frank Calegari and Akshay Venkatesh. Lifting the Hasse invariant 20 2. 8, 1235–1346. The above results imply the easily observed 2 FRANK CALEGARI AND QIANKANG CHEN Then ∆ is isomorphic to a cocompact subgroup of PSL 2(R). The Mahler lectures are a biennial activity organised by the Australian Mathematical Society, and supported by the Australian Mathematical Sciences Institute. Introduction Assume (for this paragraph only) the standard conjectures, and suppose that Mis a pure (with Frank Calegari) Algebra Number Theory 8 (2014), no. Dimitrov and Y. ROBERTS Abstract. Jump to navigation Jump to search. Eckhart Hall 5734 S University Ave Chicago IL, 60637 773 702 7100 FRANK CALEGARI, DAVID GERAGHTY, AND MICHAEL HARRIS Contents 1. 2140/obs. Frank Calegari was born on December 15, 1975. Other writing Authors: Frank Calegari, Shiva Chidambaram, David P. -12:00 p. Frank Calegari Let K be an arbitrary number field, and let ρ : Gal(/ K) → GL 2 (E) be a nearly ordinary irreducible geometric Galois representation. We prove the existence of a cuspidal automorphic representation π for GL79/Q of level one and weight zero. J. Abstract. [1] He has both Australian and American citizenship. Toby Gee. Given a genus two curve X : y2 = x5 + ax3 + bx2 + cx + d, we give an explicit parametrization of all other such curves Y with a speci ed symplectic isomorphism on three-torsion of Jacobians Jac(X)[3] ˘=Jac(Y )[3]. So when in 2012, two mathematicians — Frank Calegari of the University of Chicago and David Geraghty (now a research scientist at Facebook) — proposed a way to overcome the obstruction to extending the Taylor-Wiles method, their idea sent ripples of excitement through the new generation of number theorists. When K is a totally real field and n = 2, many cases of Conjecture 1. The Frobenius morphism 18 1. 5 were given by Frank Calegari and David Geraghty in [CG18, Corol-lary 1. Veja o perfil de Jacson Frank Calegari Secato no LinkedIn, uma comunidade profissional de 1 bilhão de usuários. Shuli Chen Dickson Instructor Subhadip Chowdhury. When K is totally real and ρ is modular, results of Hida imply that the nearly ordinary deformation space associated to ρ contains a Zariski dense set of points A recent proof by Frank Calegari and two co-authors will, mathematicians hope, usher in a gold rush of new results on the irrationality of numbers. Frank Calegari Associate Chair, Professor Justin Campbell. 2 FRANK CALEGARI AND QIANKANG CHEN Then ∆ is isomorphic to a cocompact subgroup of PSL 2(R). E-mail: fcale@math. Semantic Scholar's Logo. Current browse context: Patrick Allen, Frank Calegari, Ana Caraiani, Toby Gee, David Helm, Bao Le Hung, James Newton, Peter Scholze, Richard Taylor, Jack Thorne Author Affiliations + Patrick Allen, 1 Frank Calegari, 2 Ana Caraiani, 3 Toby Gee, 4 David Helm, 4 Bao Le Hung, 5 James Newton, 6 Peter Scholze, 7 Richard Taylor, 8 Jack Thorne 9 John Tate (March 13, 1925 – October 16, 2019) was one of the most influential mathematicians of the 20th century. Event photo g Download Citation | On Dec 15, 2023, Frank Calegari published Reciprocity in the Langlands program since Fermat’s Last Theorem | Find, read and cite all the research you need on ResearchGate From: Frank Calegari Tue, 17 Jul 2012 22:01:45 UTC (66 KB) [v2] Sun, 16 Jul 2017 01:17:28 UTC (116 KB) Full-text links: Access Paper: View a PDF of the paper titled Modularity Lifting beyond the Taylor-Wiles Method, by Frank Calegari and David Geraghty. According to our current on-line database, Francesco Calegari has 9 students and 9 descendants. 2, pp. Here are web pages of my students. Students. Tang) Finite groups whose real irreducible representations have unique dimensions. Fields of definition for triangle groups as Fuchsian groups. 4 (2020), No. 150 (2014), no. My research is in the area of algebraic number theory. View PDF Abstract: We prove the modularity of a positive proportion of FRANK CALEGARI Contents 1. 6. [1]He won a bronze medal and a silver medal at the International Mathematical Olympiad while representing Australia in 1992 and 1993 respectively. View PDF HTML (experimental) Abstract: We prove the unbounded denominators conjecture in the theory of noncongruence modular forms for finite index subgroups of SL_2(Z). View PDF Abstract: We study torsion in the homology of arithmetic groups and give evidence that it plays a role in the Langlands program. 321, p 387-394. Our result includes also Mason's generalization of the original conjecture to the setting of vector-valued modular forms, thereby supplying a new path to the congruence property in rational conformal field theory. FRANK CALEGARI Abstract. The proof I’m advised by Professor Frank Calegari and Professor Janos Simon. Now it’s finally By Frank Calegari, Northwestern University, Matthew Emerton, Northwestern University Edited by John Coates, University of Cambridge, Minhyong Kim, University College London, Florian Pop, University of Pennsylvania, Mohamed Saïdi, University of Exeter, Peter Schneider; Book: Non-abelian Fundamental Groups and Iwasawa Theory Frank Calegari (with Vesselin Dimitrov and Yunqing Tang) Why Grothendieck and computers are best of friends. (with T. Eletricista na Churrasqueiras Lobo · Experiência: Churrasqueiras Lobo · Formação acadêmica: senai · Localidade: Nova Venécia. de l'IHES (to appear) pdf: 43: Frank Calegari and Matthew Emerton: Globally realizable components of local FRANK CALEGARI 1. And discover all it Frank Calegari 1 Introduction Apery’s proof´ [13]of the irrationality of ζ(3) is now over 25 years old,and it is perhaps surprising that his methods have not yielded any significant new results (although fur-ther progress has been made on the irrationality of zeta values [1,14]). Frank Calegari (Q66058234) From Wikidata. View PDF Frank Calegari; Published 29 September 2021; Mathematics; This is a survey article on developments in modularity since the proof of Fermat's Last Theorem, with an emphasis on the historical development of the subject rather than any technical details. We welcome any additional information. edu Authors: Frank Calegari, Stavros Garoufalidis, Don Zagier. 2. 2020. 418 FRANK CALEGARI AND MATTHEW EMERTON Isr. Allen, Frank Calegari, Ana Caraiani, Toby Gee, David Helm, Bao V. p-adic modular forms: The Serre Speaker: Frank Calegari Title: The modularity of genus two curves Abstract: In his celebrated work on Fermats Last Theorem, Wiles introduced a fundamental new idea (the Taylor-Wiles method) for relating objects in arithmetic geometry (genus one curves over Q and their point counts modulo p for all primes p) to analysis (modular forms). Preprints. He works on algebraic number theory, especially the Langlands programme and Francesco Damien "Frank" Calegari is a professor of mathematics at the University of Chicago working in number theory and the Langlands program. We furthermore show the modularity of infinitely many abelian surfaces A over Q with End_C(A)=Z. 7. Office hours: Tue, 11:00–12:00, Thurs, 2:00–3:00, and by Frank Calegari, a mathematician at the University of Chicago, studies modular forms and related mathematical objects. (with V. Francesco Damien "Frank" Calegari is a professor of mathematics at the University of Chicago working in number theory and the Langlands program. Links. 8. 2023. Mathematics of Computation (89) 2020, no. It is known that under certain conditions modularity of X implies Frank Calegari Semistable abelian varieties over Q Received: 2 October 2002 / Revised Version: 17 November 2003 Published online: 3 March 2004 Abstract. Unité de Mathématiques pures et appliquées, Ecole normale supérieure de Lyon, 46 allée d’Italie, 69 364, About Press Copyright Contact us Creators Advertise Developers Terms Privacy Policy & Safety How YouTube works Test new features NFL Sunday Ticket Press Copyright Hello, This blog is intended to be a supplement to Math 16100 at the University of Chicago for Fall of 2024 as taught by Frank Calegari. The Cartier operator on curves 19 1. Justin Campbell Dickson Instructor Noah Caplinger. arXiv; Modularity of nearly ordinary 2-adic residually dihedral Galois representations. DOI: 10. Skip to search form Skip to main content Skip to account menu. 5 were proved by Patrick B. 3. Y1 - 2020. Kapil Chandran. cirm-math. Calegari: Department of Mathematics, Harvard University, Cambridge, MA 02138, USA. Chen) The linear independence of 1, ζ(2), and L(2,χ-3). Vanishing Theorems 4 3. Visions in Arithmetic and Beyond: Celebrating Peter Sarnak's Work and ImpactJune 6, 2024Starting with the "Leibniz" formula for ππ/4=1−1/3+1/5−1/7+the speci Here is an exposition of our work by Frank Calegari. Menu: Main page; Research; Teaching; Editorial Boards; Students; Diversions; Schedule; 2024-2025. Department of Mathematics, Imperial College London, London, SW7 2AZ, UK. We prove the unbounded denominators conjecture in the theory of noncongruence modular forms. F. View PDF; TeX Source; Other Formats; view Math 124, Number Theory Instructor: Frank Calegari, 432 Science Center. These days I mostly think about number theory, but in the past I studied quantum computers, worked on mixed reality headsets, and did some not-math competitions. Menu: Main page; Research; Teaching; Editorial Boards; Students; Diversions; Schedule; My research interests include the theory of Galois representations (particularly the problem of reciprocity in the Langlands program), the cohomology of arithmetic groups, and more recently the arithmetic of periods. Relation with special values of periods 3 3. We prove the unbounded denominators conjecture in the theory of noncongruence modular forms for finite index subgroups of SL_2(Z). 1. Some modular abelian surfaces, with F. (with Q. PY - 2020. 4171/OWR/2021/18 Mathematics Subject Classification. edu. H. We show that abelian surfaces (and consequently curves of genus 2) over totally real fields are potentially modular. 4. Roberts Given a genus two curve X : y2 = x5 +ax3 +bx2 +cx+d, we give an explicit parametrization of all other such curves Y with a specified symplectic isomorphism on three-torsion of Jacobians Jac(X)[3] ⇠= Jac(Y)[3]. I am on the job market this year. Pages 897-1113 from Volume 197 (2023), Issue 3 by Patrick B. Office: Science Center 432 Office Phone: 495-8796 Office Hours: My fall 2003 office hours are: Tue, 11:00-12:00, Thurs, 2:00-3:00. pdf. We prove, under mild hypotheses, that there are no irreducible two-dimensional or-dinary even Galois representations of Gal(Q/Q) with distinct Hodge-Tate weights. Authors: Frank Calegari, Matthew Emerton. Some items. Roberts: Vol. The lecture took place at the University Frank Calegari, D. His research interests include geometry , dynamical systems , low-dimensional topology , and geometric group theory . Prerequisites: Mathematics 122 (which may be taken concurrently) or equivalent. Ghitza. Francesco Damien "Frank" Calegari, né le 15 décembre 1975 , est un mathématicien australien et américain, professeur de mathématiques à l'Université de Chicago ; il travaille en théorie des nombres des nombres et sur le programme de Langlands. Early life and education. [2] Calegari received his PhD in mathematics from the University of California, Berkeley in 2022 Mahler Lecturer. Basics 1 1. Frank Calegari. DIMITROV, AND Y. The reciprocity conjecture in the Langlands program links motives to automorphic forms. 18 (2021), no. Oberwolfach Rep. If α= a/b ∈Q, and α̸= p/q; The Southwest Center for Arithmetic Geometry. I am a graduate student at the University of Chicago under the supervision of Professor Frank Calegari. Navarro, and P. Compositio Math. 197. The Bost–Charles bound97 7. What is a modular form? 4 1. DOI 10. In Autumn 2024, I will be teaching two streams of Math 16100, honours (or honors) calculus. 91. Allen and Frank Calegari, following from the result of [PS16], see [AC14, Corollary 3]. 24), (4. Shuli Chen. A brief review of Bost’s slopes method94 7. Search. We also deduce FRANK CALEGARI, SHIVA CHIDAMBARAM, AND DAVID P. Roberts. McMullen asks for which n these functions Frank Calegari, Shiva Chidambaram, and David P. It is well known (see [Tak77, Prop 1]) that the embedding ∆ ,→PSL 2(R) is unique up to conjugation and (as a FRANK CALEGARI, VESSELIN DIMITROV, AND YUNQING TANG 2 F. Proofs 7 References 9 1. This book chapter is published open access. Breuer, S. Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library. View a PDF of the paper titled Abelian surfaces with fixed $3$-torsion, by Frank Calegari and 2 other authors. The q-expansion priniciple 14 1. Here is my CV. Original design by Andreas ViklundAndreas Viklund Esteemed algebraic number theorist Professor Frank Calegari gave a public talk titled ‘The secrets of Pi (and other transcendental numbers)’ on 23 November 2022, hosted by SMRI. Calegari besuchte die Schule und Universität (Bachelor-Abschluss) in Melbourne [2] und wurde 2002 bei Kenneth Ribet an der University of California, Berkeley, promoviert (Ramification and View a PDF of the paper titled Reciprocity in the Langlands program since Fermat's Last Theorem, by Frank Calegari Frank Calegari is a professor of mathematics at the University of Chicago and Northwestern University. Math. 4007/annals. We give a necessarily set of criteria for m_E to be odd. I am particularly interested in the Langlands programme, especially, the notion of reciprocity linking Galois representations and motives to automorphic forms. . fr. View PDF; HTML (experimental) TeX Source; Other Formats; view license. If you have additional information or corrections regarding this mathematician, please use the update form. We establish some new cases of Artin’s conjecture. Calegari and A. Betti Cohomology 4 3. If K/Q is Schedule: (2019): I'm mostly busy for the next 18 years. After graduating from the University of Melbourne he took his PhD at the University of California, Berkeley. Many mathematicians take an Occam’s-razor point of Frank Calegari; Published 16 August 2004; Mathematics; arXiv: Number Theory; Following Apery's proof of the irrationality of zeta(3), Beukers found an elegant reinterpretation of Apery's arguments using modular forms. In practice, this imposes several George Boxer, Frank Calegari and Vincent Pilloni: Abelian Surfaces over totally real fields are potentially modular: Publ. Abstract: Given a genus two curve X: y 2 = x 5 + a x 3 + b x 2 + c x + d, we give an explicit parametrization of all other such curves Y with a specified symplectic isomorphism on three-torsion of Jacobians Jac (X) [3] ≅ Jac Patrick Allen, Frank Calegari, Ana Caraiani, Toby Gee, David Helm, Bao Le Hung, James Newton, Peter Scholze, Richard Taylor, Jack Thorne Author Affiliations + Patrick Allen, 1 Frank Calegari, 2 Ana Caraiani, 3 Toby Gee, 4 David Helm, 4 Bao Le Hung, 5 James Newton, 6 Peter Scholze, 7 Richard Taylor, 8 Jack Thorne 9 Semantic Scholar profile for Frank Calegari, with 100 highly influential citations and 83 scientific research papers. 2, 212–216. 9, 2263–2272. Esteemed algebraic number theorist Professor Frank Calegari presented this public talk on the Secrets of Pi on 23 November 2022, hosted by SMRI. Professor Frank Calegari, The University of Chicago. George Boxer & Frank Calegari. 310 Science Center. The unbounded denominators conjecture, with Frank Calegari and Yunqing Tang. It is well known (see [Tak77, Prop 1]) that the embedding ∆ ,→PSL 2(R) is unique up to conjugation and (as a Explicit Serre weights for two-dimensional Galois representations (with Frank Calegari, Toby Gee, and Lambros Mavrides) Appeared in Comp. m. View PDF Abstract: Following Apery's proof of the irrationality of zeta(3), Beukers found an elegant reinterpretation of Apery's arguments using modular forms. ) Frank Calegari The Artin conjecture for some S 5-extensions Frank Calegari Received: 5 January 2012/Revised: 4 July 2012 – c Springer-Verlag 2013 Abstract. Francesco Damien Calegari; Francesco Calegari; edit. 6]. harvard. Subhadip Chowdhury Frank Calegari, Shiva Chidambaram and David P. Improvements from convexity91 7. AU - Calegari, Frank. Introduction In this paper, we prove non-minimal modularity lifting theorem for ordinary Galois repre-sentations over imaginary quadratic fields. e-mail: fcale@math. Number Theory 126 (2007), no. 5. 4171/OWR/2021/18. View a PDF of the paper titled Modularity theorems for abelian surfaces, by George Boxer and 3 other authors. Language Label Description Also known as; default for all languages: GEORGE BOXER, FRANK CALEGARI, AND TOBY GEE To Laurent Clozel, in admiration. The convexity enhancement of the Bost–Charles bound105 7. CALEGARI, V. The classes will run MWF at 10:30-11:20 and MWF 11:30-12:20. 16100 course web page; I am a Professor at the University of Chicago. N2 - People often value an item more when they own it than when it is available for purchase, and consequently are relatively reluctant to trade. Our first theorem is as follows: Theorem 1. We show how Authors: Frank Calegari, Akshay Venkatesh. The Hasse invariant 18 1. Hecke operators 14 1. Frank Calegari is a mathematician at the University of Chicago who works on the Langlands programme and reciprocity. We construct π using symmetric power functoriality and a change of weight theorem, using Galois deformation theory. Le Hung, James Newton, Peter Scholze, Richard Taylor, Jack A. My research is in the area of algebraic number theory, especially the computation of deformation rings. As a consequence, we obtain the expected meromorphic continuation and functional equations of their Hasse– Weil zeta functions. #2. He has a blog, a contact page, and a brother named Danny Calegari. I’m supported by We show that abelian surfaces (and consequently curves of genus 2) over totally real fields are potentially modular. Jayne Ion “It’s something that’s been in the air for decades,” Bost said. wfji vbjpf fkbrzb afyrk mwmvqd ljblhs bbn nsc cwazh zyvrj lcehp revaedb hxbc tjfwbof vsgt