photo  



Gonçalo Nery Tabuada



Mathematics Institute
Zeeman Building
University of Warwick
Coventry CV4 7AL
United Kingdom

goncalo.tabuada@warwick.ac.uk
Office: C1.23


 
[Preprints]
[Publications]

[Surveys]
[Books]
[Talks]
[Videos]









[Preprints]


Noncommutative Riemann hypothesis [pdf]


Motivic Atiyah-Segal completion theorem [pdf]
with Michel Van den Bergh


Noncommutative Weil conjecture [pdf]


Jacques Tits motivic measure [pdf]
To appear in Mathematische Annalen



HPD-invariance of the Tate conjecture(s) [pdf]
To appear in Journal of Noncommutative Geometry





[Publications]


Schur-finiteness (and Bass-finiteness) conjecture for quadric fibrations and for families of sextic du Val del Pezzo surfaces [link]
Documenta Mathematica, 25 (2020), 2339-2354


Embedding of the derived Brauer group into the secondary K-theory ring [link]

Journal of Noncommutative Geometry, 14 (2020), 773-788


Motivic concentration theorem [link]
with Michel Van den Bergh
Mathematical Research Letters, 27 (2020), no. 2, 565-589


Noncommutative motives in positive characteristic and their applications [link]
Advances in Mathematics, 349 (2019), 648-681


Vanishing of the negative homotopy K-theory of quotient singularities [link]
Journal of the Institute of Mathematics of Jussieu, 18 (2019), no. 3, 619-627


On Grothendieck's standard conjectures of type C and D in positive characteristic [link]
Proceedings of the American Mathematical Society 147 (2019), no. 12, 5039-5054


Feynman quadrics-motive of the massive sunset graph [link]
with Matilde Marcolli
Journal of Number Theory, 195 (2019), 159-183


A note on the Schur-finiteness of linear sections [link]
Mathematical Research Letters, 25 (2018), no. 1, 237-253


Invariants of noncommutative projective schemes [link]
Moscow Mathematical Journal, 18 (2018), no. 4, 787-797


Noncommutative rigidity [link]
Mathematische Zeitschrift, 289 (2018), no. 3, 1281-1298


A note on Grothendieck's standard conjectures of type C and D [link]
Proceedings of the American Mathematical Society, 146 (2018), no. 4, 1389-1399


Equivariant noncommutative motives [link]
Annals of K-theory, 3 (2018), no. 1, 125-156


Additive invariants of orbifolds [link]
with Michel Van den Bergh
Geometry and Topology, 22 (2018), 3003-3048


Some remarks concerning Voevodsky's nilpotence conjecture [link]
with Marcello Bernardara and Matilde Marcolli
Journal für die reine und angewandte Mathematik, 738 (2018), 299-312


The Gysin triangle via localization and A^1-homotopy invariance [link]
with Michel Van den Bergh
Transactions of the American Mathematical Society, 370 (2018), no. 1, 421-446


Modified mixed realizations, new additive invariants, and periods of dg categories [link]
International Mathematics Research Notices, 34 (2017), 7607-7638


A^1-homotopy invariance of algebraic K-theory with coefficients and du Val singularities [link]
Annals of K-theory, 2 (2017), no. 1, 1-25


Kimura-finiteness of quadric fibrations over smooth curves [link]
C. R. Math. Acad. Sci. Paris, 355 (2017), 628-632
(presented by Christophe Soulé)


A^1-homotopy invariants of corner skew Laurent polynomial algebras [link]
Journal of Noncommutative Geometry 11 (2017), no. 4, 1627-1643


Picard groups, weight structures, and (noncommutative) mixed motives [link]
with Mikhail Bondarko
Documenta Mathematica 22 (2017), 45-66


Bost-Connes systems, Categorification, Quantum statistical mechanics, and Weil numbers [link]
with Matilde Marcolli
Journal of Noncommutative Geometry 11 (2017), no. 1, 1-49


A note on secondary K-theory [link]
Algebra and Number Theory, 10 (2016), no. 4, 887-906


Noncommutative mixed (Artin) motives and their motivic Hopf dg algebras [link]
Selecta Mathematica, 22 (2016), no. 2, 735-764


Algebraic K-theory with coefficients of cyclic quotient singularities [link]
C. R. Math. Acad. Sci. Paris, 354 (2016), 449-452
(presented by Michel Duflo)


Noncommutative numerical motives, Tannakian structures, and motivic Galois groups [link]
with Matilde Marcolli
Journal of the European Mathematical Society 18 (2016), 623-655


Noncommutative motives of separable algebras [link]
with Michel Van den Bergh
Advances in Mathematics, 303 (2016), 1122-1161


 K-theory of endomorphisms via noncommutative motives [link]
 with Andrew Blumberg and David Gepner
Transactions of the American Mathematical Society 368 (2016), no. 2, 1435-1465


From semi-orthogonal decompositions to polarized intermediate Jacobians via Jacobians of noncommutative motives [link]
with Marcello Bernardara
Moscow Mathematical Journal, 16 (2016), no. 2, 205-235


Chow groups of intersections of quadrics via homological projective duality and (Jacobians of) noncommutative motives [link]
with Marcello Bernardara
Izv. Ross. Akad. Nauk. Ser. Mat. 80 (2016), no. 3, 3-22


A^1-homotopy theory of noncommutative motives [link]
Journal of Noncommutative Geometry 9 (2015), no. 3, 851-875


Bivariant cyclic cohomology and Connes' bilinear pairings in noncommutative motives [link]
Journal of Noncommutative Geometry 9 (2015), no. 2, 265-285


Exponentiation of motivic measures [link]
with Niranjan Ramachandran
Journal of the Ramanujan Mathematical Society 30, (2015), no. 4, 349-360


Weil restriction of noncommutative motives [link]
Journal of Algebra, 430 (2015), 119-152


A^1-homotopy invariants of dg orbit categories [link]
Journal of Algebra, 434 (2015), 169-192


From exceptional collections to motivic decompositions via noncommutative motives [link]
with Matilde Marcolli
Journal für die reine und angewandte Mathematik 701 (2015), 153-167


Unconditional noncommutative motivic Galois groups [link]
with Matilde Marcolli
Hodge theory and classical algebraic geometry. Contemporary Mathematics 647 (2015), 109-115


Noncommutative motives of Azumaya algebras [link]
with Michel Van den Bergh
Journal of the Institute of Mathematics of Jussieu, 14 (2015), no. 2, 379-403


Relations between the Chow motive and the noncommutative motive of a smooth projective variety [link]
with Marcello Bernardara
Journal of Pure and Applied Algebra, 219 (2015), no. 11, 5068-5077


Voevodsky's mixed motives versus Kontsevich's noncommutative mixed motives [link]
Advances in Mathematics, 264 (2014), 506-545


Additive invariants of toric and twisted projective homogeneous varieties via noncommutative motives [link]
Journal of Algebra, 417 (2014), 15-38


A Quillen model for classical Morita theory and a tensor categorification of the Brauer group [link]
with Ivo Dell'Ambrogio
Journal of Pure and Applied Algebra, 218 (2014), no. 12, 2337-2355


Uniqueness of the multiplicative cyclotomic trace [link]
 with Andrew Blumberg and David Gepner
Advances in Mathematics, 260 (2014), 191-232


Jacobians of noncommutative motives [link]
with Matilde Marcolli
Moscow Mathematical Journal, 14 (2014), no. 3, 577-594


Galois descent of additive invariants [link]
Bulletin of the London Mathematical Society, 46 (2014), no. 2, 385-395


E_n-regularity implies E_(n-1)-regularity [link]
Documenta Mathematica, 19 (2014), 121-139


Witt vectors and K-theory of automorphisms via noncommutative motives [link]
Manuscripta Mathematica, 143 (2014), no. 3-4, 473-482


Noncommutative motives, numerical equivalence, and semi-simplicity [link]
with Matilde Marcolli
American Journal of Mathematics, 136 (2014), no. 1, 59-75


Noncommutative Artin motives [link]
with Matilde Marcolli
Selecta Mathematica, 20 (2014), 315-358


Morita homotopy theory of C*-categories [link]
with Ivo Dell'Ambrogio
Journal of Algebra, 398 (2014), 162-199


Lefschetz and Hirzebruch-Riemann-Roch formulas via noncommutative motives [link]
with Denis-Charles Cisinski
Journal of Noncommutative Geometry 8 (2014), no. 4, 1171-1190


Chow motives versus noncommutative motives [link]
Journal of Noncommutative Geometry 7 (2013), no. 3, 767-786


Fundamental isomorphism conjecture via noncommutative motives [link]
with Paul Balmer
Mathematische Nachrichten, 286 (2013), no. 8-9, 791-798


A universal characterization of higher algebraic K-theory [link]
with Andrew Blumberg and David Gepner
Geometry and Topology, 17 (2013), 733-838


Weil cohomologies and derived dg categories [link]
Journal of Pure and Applied Algebra, 217 (2013), 1294-1302


Products, multiplicative Chern characters, and finite coefficients via noncommutative motives [link]
Journal of Pure and Applied Algebra, 217 (2013), 1279-1293


Kontsevich's noncommutative numerical motives [link]
with Matilde Marcolli
Compositio Mathematica, 148 (2012), 1811-1820


Weight structure on Kontsevich's noncommutative mixed motives [link]
Homology, Homotopy and Applications, 14(2) (2012), 129-142


The fundamental theorem via derived Morita invariance, localization, and A^1-homotopy invariance [link]
Journal of K-Theory, 9 (2012), no. 3, 407-420


Transfer maps and projection formulas [link]
Proceedings of the American Mathematical Society, 140 (2012), 2589-2597


Symmetric monoidal structure on noncommutative motives [link]
with Denis-Charles Cisinski
Journal of K-Theory, 9 (2012), no. 2, 201-268


Tensor triangular geometry of noncommutative motives [link]
with Ivo Dell'Ambrogio
Advances in Mathematics, 229 (2012), no. 2, 1329-1357


Co-representability of the Grothendieck group of endomorphisms functor in the category of noncommutative motives [link]
Homology, Homotopy and Applications, 13(2) (2011), 315-328


Universal suspension via noncommutative motives [link]
Journal of Noncommutative Geometry 5 (2011), no. 4, 573-589


A simple criterion for extending natural transformations to higher K-theory [link]
Documenta Mathematica 16 (2011), 657-668


Nonconnective K-theory via universal invariants [link]
with Denis-Charles Cisinski
Compositio Mathematica 147 (2011), 1281-1320


A universal characterization of the Chern character maps [link]
Proceedings of the American Mathematical Society 139 (2011), 1263-1271


On Drinfeld's DG quotient [link]
Journal of Algebra, 323 (2010), 1226-1240


Homotopy theory of dg categories via localizing pairs and Drinfeld's DG quotient [link]
Homology, Homotopy and Applications, 12(1) (2010), 187-219


Matrix invariants of spectral categories [link]
International Mathematics Research Notices, 13 (2010), 2459-2511


Generalized spectral categories, topological Hochschild homology, and trace maps [link]
Algebraic and Geometric Topology, 10 (2010), 137-213


Differential graded versus simplicial categories [link]
Topology and its Applications, 157 (2010), no. 3, 563-593


Postnikov towers, k-invariants and obstruction theory for dg categories [link]
Journal of Algebra, 321 (2009), no. 12, 3850-3877


Homotopy theory of spectral categories [link]
Advances in Mathematics, 221 (2009), no. 4, 1122-1143


Noncommutative André-Quillen cohomology for differential graded categories [link]
Journal of Algebra, 321 (2009), no. 10, 2926-2942


Homotopy theory of well-generated algebraic triangulated categories [link]
Journal of K-Theory, 3 (2009), no. 1, 53-75


Higher K-theory via universal invariants [link]
Duke Mathematical Journal, 145 (2008), no. 1, 121-206


On the structure of Calabi-Yau categories with a cluster tilting subcategory [link]
Documenta Mathematica, 12 (2007), 193-213


Additive invariants of dg categories [link]
International Mathematics Research Notices 53 (2005), 3309-3339
Addendum: International Mathematics Research Notices (2006), Art. ID 75853
Errata: International Mathematics Research Notices 24 (2007), Art. ID rnm149
(in french)


A Quillen model structure on the category of dg categories [link]
C. R. Math. Acad. Sci. Paris, 340 (2005), 15-19
(presented by Christophe Soulé)
(in french)





[Surveys]


Noncommutative counterparts of celebrated conjectures [link]
K-theory in Algebra, Analysis and Topology (satellite event of the ICM 2018)
Contemporary Mathematics
 749 (2020),
353-377


Recent developments on noncommutative motives [link]
New Directions in Homotopy Theory, Contemporary Mathematics 707 (2018), 143-173


Noncommutative motives and their applications [link]
with Matilde Marcolli

Commutative Algebra and Noncommutative Algebraic Geometry I, MSRI Publications 67 (2015), 191-214


A guided tour through the garden of noncommutative motives [link]
Clay Mathematics Proceedings, 16 (2012),
259-276





[Books]


Noncommutative Motives
(with a preface by Yuri I. Manin) [link]
University Lecture Series 63, American Mathematical Society, 2015





[Talks]


Conference Witt vectors in Algebra and Geometry,
Moscow, Russia
October 2022


Conference Noncommutative shapes (in honor of Michel Van den Bergh's 61th birthday), Antwerp, Belgium
September 2022


Workshop Homotopical Algebra and Higher Structures,
Oberwolfach, Germany
September 2021


Portuguese Mathematical Society meeting (80th
birthday celebration), Lisbon, Portugal
July 2021


Noncommutative Geometry and Topology seminar,
Czech Academy of Sciences, Prague, Czech Republic
June 2021


New York City Noncommutative Geometry seminar, New York, United States
January 2021


Workshop Noncommutative motives and telescope-type problems, Hausdorff Research Institute for Mathematics, Bonn, Germany
December 2020


Algebraic Topology seminar, University of Warwick, United Kingdom
December 2020


Seminar on Algebra, Geometry and Physics, Max-Planck-Institut für Mathematik, Germany
August 2020


Summer school Motivic, equivariant, and noncommutative homotopy theory, IHÉS, France
(Three-lecture course)
July 2020


JAMI Workshop Riemann-Roch in characteristic one and related topics, Johns Hopkins University, United States
October 2019


Conference The geometry of derived categories, Liverpool, United Kingdom
September 2019


Workshop Algebraic K-theory, Oberwolfach, Germany
June 2019


Algebraic Geometry seminar, University of Warwick, United Kingdom
January 2019


Colloquium, University of Toronto, Canada
January 2019


Colloquium, Yale University, United States
November 2018


Algebraic and Tropical Geometry seminar, Yale University, United States
November 2018


Conference Equivariant and motivic homotopy theory, Isaac Newton Institute, Cambridge, United Kingdom
August 2018


Algebra and Number theory day, Johns Hopkins University, United States
April 2018


Arbeitsgemeinschaft: Topological Cyclic Homology, Oberwolfach, Germany
April 2018


Algebra and Topology seminar, Université Strasbourg, France
January 2018


Colloquium, University of California at Santa Barbara, United States
January 2018


Colloquium, University of California at San Diego, United States
December 2017


Conference Vector bundles and algebraic curves (VBAC 2017), Essen, Germany
(Four-lecture course)
September 2017


Mathematische Arbeitstagung 2017 (in honor of Yuri I. Manin's 80th birthday), Max-Planck-Institut für Mathematik, Bonn, Germany
June 2017


Workshop K-theory in algebraic geometry and number theory, Hausdorff Research Institute for Mathematics, Bonn, Germany
May 2017


Conference Algebro-Geometric and Homotopical Methods, Institut Mittag-Leffler, Sweden
March 2017


Colloquium, University of Southern California, United States
February 2017


Colloquium, Institut de Mathématiques de Jussieu, Paris, France
January 2017


Algebraic Topology seminar, Université Paris 13, France
January 2017


Conference Noncommutative, derived and homotopical methods in geometry, Antwerp, Belgium
September 2016


International K-theory Conference, Sydney, Australia
August 2016


Conference Interacting Algebraic Geometry, Dijon, France
July 2016


Workshop Algebraic K-theory and motivic cohomology, Oberwolfach, Germany
June 2016


Workshop Triangulated Categories and Applications, Banff Institute, Canada
June 2016


Geometry, physics, and representation theory seminar, Northeastern University, United States
April 2016


Conference Mid-Atlantic Topology, Johns Hopkins University, United States
March 2016


Conference Motives, Tokyo, Japan
February 2016


Algebraic Geometry seminar, Università degli Studi di Milano, Italy
July 2015


Colloquium, University of California at Los Angeles, United States
February 2015


Workshop Cohomological Realizations of Motives, Banff Institute, Canada
December 2014


Colloquium, University of Maryland, United States
October 2014


Algebra and Number Theory seminar, University of Maryland, United States
October 2014


Conference K-theory and related topics, Beijing, China
August 2014


Conference Reimagining the Foundations of Algebraic Topology, MSRI, Berkeley, United States
April 2014


Algebraic Geometry seminar, California Institute of Technology, United States
January 2014


Colloquium, California Institute of Technology, United States
January 2014


Infinite Dimensional Algebraic Geometry seminar, Yale University, United States
September 2013


Conference Homotopical methods in algebraic geometry, University of Southern California, United States
June 2013


Colloquium, University of California, Berkeley, United States
May 2013


Conference Interactions between Noncommutative Algebra and Algebraic Geometry, MSRI,
Berkeley, United States
April 2013


Conference Motives, Tokyo, Japan
December 2012


Conference Algebraic Topology, Arolla, Switzerland
August 2012


Conference Periods and Motives, Madrid, Spain
July 2012


Conference Noncommutative Algebraic Geometry and its Applications to Physics, Leiden, Netherlands
March 2012


Colloquium, California Institute of Technology, United States
January 2012


Algebraic Topology seminar, Massachusetts Institute of Technology, United States
November 2011


Seminar on Algebra, Geometry and Physics, Max-Planck-Institut für Mathematik, Germany
July 2011


Conference Triangulated categories and applications, Banff Institute, Canada
June 2011


Representation Theory seminar, Northeastern University, United States
April 2011


Midwest Topology conference, University of Chicago, United States
April 2011


Geometric Langlands seminar, University of Chicago, United States
April 2011


Noncommutative Geometry seminar, California Institute of Technology, United States
March 2011

 
Noncommutative Algebraic Geometry seminar, Massachusetts Institute of Technology, United States
January 2011


Conference Homotopy theory and derived algebraic geometry, Fields Institute, Toronto, Canada
August 2010


Conference Topics in Noncommutative Geometry, Buenos Aires, Argentine
July 2010


Algebraic Topology seminar, Northwestern University, United States
May 2010


Algebraic Topology seminar, University of Illinois at Urbana-Champaign, United States
April 2010


Algebraic Topology seminar, University of Chicago, United States
April 2010


Algebraic Topology seminar, Massachusetts Institute of Technology, United States
March 2010


Algebraic Topology seminar, Stanford University, United States
May 2009


Algebra seminar, University of California at Los Angeles, United States
May 2009


Conference Cats 3, Centro di Ricerca Matematica Ennio De Giorgi, Pisa, Italy
September 2008


Algebraic Topology seminar,  University of Bonn, Germany
July 2008


 Conference Homotopy Structures in Geometry and Algebra, Centre de Recerca Matemàtica, Barcelona, Spain
June 2008


Algebra seminar, Laboratoire J. A. Dieudonné, Nice, France
April 2008





[Videos]



Noncommutative Riemann hypothesis [link]

Noncommutative Geometry and Topology seminar (2021)
Czech
Academy of Sciences, Prague, Czech Republic


Noncommutative Weil conjecture [link]
NYC Noncommutative geometry seminar (2021)
New York, United States


Jacques Tits motivic measure [link]
Workshop Noncommutative motives and telescope-type problems (2020)
Hausdorff Research Institute for Mathematics, Bonn, Germany


Motivic Atiyah-Segal completion theorem [link]
Algebraic topology seminar (2020)
University of Warwick, United Kingdom


Noncommutative counterparts of celebrated conjectures [link]
Summer school Motivic, equivariant, and noncommutative homotopy theory (2020)
Institut des Hautes Études Scientifiques, France


Grothendieck's standard conjectures via noncommutative algebraic geometry [link]
Mathematische Arbeitstagung 2017 (in honor of Yuri I. Manin's 80th birthday)
Max-Planck-Institut für Mathematik, Bonn, Germany
 

Additive invariants of orbifolds [link]
Conference K-theory in algebraic geometry and number theory (2017)
Hausdorff Research Institute for Mathematics, Bonn, Germany


Noncommutative motives of separable algebras [link]
Conference Cohomological realizations of motives (2014)
Banff International Research Station for Mathematical Innovation and Discovery, Canada


Motives versus noncommutative motives [link]
Conference Reimagining the foundations of algebraic topology (2014)
Mathematical Sciences Research Institute, Berkeley, United States


Noncommutative motives [link]
Conference Interactions between noncommutative algebra, representation theory, and algebraic geometry (2013)
Mathematical Sciences Research Institute, Berkeley, United States