3900 N. Charles St. 1303 Baltimore, MD 21218 USA T +1 410 599-4686 Caterina Consani H +39 348 0328694 B [email protected] Curriculum Vitæ Í www.math.jhu.edu/~kc

Personal Data Name Caterina Surname Consani Place and date of birth Chiavari (Genoa) Italy, January 9, 1963 Nationality Italian Residence United States of America Languages English (fluent), French (fluent), Italian. Studies 1993-96 Ph.D in Mathematics Department of Mathematics, (USA) Research in: arithmetic geometry, algebraic number theory. Thesis title: “Double complexes and Euler L-factors on degenerations of algebraic varieties”. Thesis adviser: Prof. 1988-92 Dottorato di Ricerca in Matematica (Ph.D in Mathematics) Universities of Genoa and Turin, Italy. Research in: algebraic geometry and algebraic K-theory. Thesis title: “Teoria dell’ intersezione e K-teoria su varietà singolari”. Thesis adviser: Prof. Claudio Pedrini 1981-86 Laurea in Matematica (Bachelor Degree in Mathematics) Department of Mathematics, University of Genoa (Italy) Graduation Grade: 110/110 Summa cum Laude. University Curriculum 2008-today Full Professor (tenured) Department of Mathematics, The (USA) 2005-08 Associate Professor (tenured) Department of Mathematics, The Johns Hopkins University (USA) 2003-05 Associate Professor (tenured) Department of Mathematics, (Canada) 2000-03 Assistant Professor (tenure track) Department of Mathematics, University of Toronto (Canada) 1999-2000 Researcher (Member of the) School of Mathematics, Institute of Advanced Study, Princeton (USA) 1998 Researcher Department of Mathematics & Newton Institute, Cambridge University (UK) 1996-99 Assistant Professor (C.L.E. Moore Instructor) Department of Mathematics, M.I.T. (USA). Visiting Positions (last 10 years) 2011-17 Collège de France (Paris, France) Visiting Professor: June-July 2011, 2012, 2013, 2016, 2017. 2017 Shanghai Center for Mathematical Sciences (China) Visiting Professor: May 2017. 2015 IHES (Paris) Visiting Professor: November 2015. 2014-15 Collège de France (Paris) Researcher (full time). 2014 Hausdorff Research Institute for Mathematics (Bonn, Germany) Visiting Professor: November 2014. 2010 RIMS University of Kyoto (Giappone) Visiting Professor: November 2010. 2008-10 IHES (Paris) Visiting Professor: June-July 2010, January 2009, January-April 2008. 2008 Fields Institute, University of Toronto (Canada) Visiting Professor: November 2008. 2008 Hausdorff Research Institute for Mathematics (Bonn) Visiting Professor: July 2008.

Research Awards 2016-17 NSF Special Meetings Grant n. 1701934 (Co-PI), JHU 2015-2020 Simons Foundation Collaboration Grant for Mathematicians n. 353677, JHU 2011-14 NSF–DMS Research Grant n. 1069218, JHU 2009-11 NSF Special Meetings Grant n. 0852421, JHU 2007-11 NSF-FRG Research Grant n. 0652431, JHU 2000-05 NSERC Research Grants nn. 72016789, 72024520, U. of Toronto 1997-2000 NSF-DMS Research Grant n. 9701302, MIT.

Selected Invited Lectures (last 10 years) 2018 Texas A&M University Invited talk at Department of Mathematics 2013-18 Ohio State University Several invited talks at Department of Mathematics: 2013, 2014, 2015, 2016, 2018 2017 Shanghai Center for Mathematical Sciences (China) Invited talk at the Meeting: “ 2017: A Celebra- tion of ’ 70th Birthday” 2015 IHES (Paris, France) Plenary talk at the Meeting: “Topos à l’IHES” 2014 Hausdorff Center for Mathematics (Bonn, Germany) Invited talk at the Meeting “Trimester Program in Noncommutative Geom- etry and its Applications” 2014 Carleton University, (Ottawa, Canada) Plenary talk at “XIII Meeting of the Canadian Number Theory Association” 2014 University of Washington St. Louis Colloquium talk at Department of Mathematics 2014 Université Paris VII (Paris) Invited talk at Department of Mathematics 2014 Université de Strasbourg (France) Invited talk at Department of Mathematics 2012 Centro de Ciencias Pedro Pascual, Benasque (Spain) Invited talk at the Meeting “Quantum Mechanics, Operator Theory and the Riemann Zeta Function" 2011 MFO Oberwolfach (Germany) Invited talk at the Meeting “Noncommutative Geometry” 2010 RIMS Kyoto (Japan) Invited talk at the Meeting “Workshop in Noncommutative Geometry and Number Theory” 2010 Utrecht University (Netherlands) Invited talks at Graduate School of Mathematics (“ Masterclass Graduate School”) 2009 Texas A&M University Invited talk at Department of Mathematics 2009 Vanderbilt University Invited talk at the Meeting “The Seventh Annual Spring Institute in Non- commutative Geometry and Operator Algebras” 2009 Fields Institute (Toronto, Canada) Invited talk at the Meeting “Arithmetic Geometry: Diophantine Approxi- mation and Arakelov Theory” 2008 Hausdorff Center for Mathematics (Bonn) Invited talk at the Meeting “Trimester Program in Geometry and Physics” 2008 University of Amsterdam (NL) Invited talk at 5ECM: Mini-Symposium in “Applications on Noncommuta- tive Geometry” 2008 Boston University Invited talk at the Meeting “Motives, Quantum Field Theory and Pseudod- ifferential Operators” 2008 Fields Institute (Toronto) Invited talk at the Meeting “Noncommutative Geometry”.

Synergistic Activities (last 10 years) 2018 Co-Organizer of the Conference “Toposes in Como” Second edition of the Conference “Topos à l’IHES” (School & Conference) Villa del Grumello, Como (Italy): 24-26 June 2018 2017 Co-Organizer of the Conference “Noncommutative Geometry: State of the Art and Future Prospects” Conference in honor of the 70th birthday of Alain Connes Fudan University, Shanghai (China) 2014 Co-Organizer of the Conference “Noncommutative Geometry – Festival” Conference in honor of the 70th birthday of Henri Moscovici University of Texas A&M. (USA) 2013 Co-Organizer of the Conference “Number-Theory and Related Topics” Conference in honor of Professor Takashi Ono. JAMI (Japan-American Mathematics Institute) Johns Hopkins University. 2011 Co-Organizer of the Conference “Non-commutative Geometry and Arithmetic” JAMI, Johns Hopkins University. 2010 Co-Organizer of the Conference “Noncommutative Geometry and Applications to Number Theory” Ohio State University. 2008-09 Co-Organizer of two Conferences on “Noncommutative Geometry and Geometry over the ” Vanderbilt University & Johns Hopkins University. 2008-09 Co-Organizer of the Conference “Arithmetic Geometry, Hyper- bolic Geometry and Related Topics” Fields Institute, University of Toronto (Canada).

Committees 2017 Member of a Graduate Board Exam (Ph.D Defense Exam) Department of Computer Sciences, Johns Hopkins University 2017 External Reviewer of a Graduate Board Exam Department of Mathematics Université Paris VII (Paris) 2014 Chair of a Graduate Board Exam Department of Computer Sciences, Johns Hopkins University 2013 External Reviewer in the Scientific Committee for a Tenure Pro- motion (full professor) Department of Mathematics, Utrecht University (NL) 2013 External Reviewer in the Scientific Committee for the review of the Department of Applied Mathematics and Statistics JHU (Whiting School of Engineering) 2011-12 Member of the Scientific Committee of the “Distinguished Awards (Non-Biomedical)” JHU 2011 Member of the Jury “Blavatnik Awards in Science” New York Academy of Sciences, New-York 2009 Member of a Graduate Board Exam Department of Physics, Johns Hopkins University. Editorial Activities 2014-today “Rendiconti del Seminario Matematico della Università di Padova” Member of the Scientific Editorial Board 2007-today “Journal of Number Theory” Member of the Scientific Editorial Board 2006-today Scientific Reviewer NSF (National Science Foundation), NSERC (Natural Sciences and En- gineering Research Council of Canada), Royal Society URF (University Research Fellowship, UK) 2005-today Scientific Reviewer Mathematical Reviews, Zentralblatt Math., Algebra and Number Theory, Americal Journal of Mathematics, Annales Sci. Math. du Québec, Canadian Journal of Mathematics, Journal of Number Theory, Journal für die Reine und Angewandte Mathematik, Journal of Algebraic Geometry, Journal of Pure and Applied Algebra, Pacific Journal of Mathematics.

Pedagogical Activities The following pedagogical activities are subdivided in three parts: teaching at the graduate level, at the College and at the Post-Graduate level.

Supervision of Ph.D Theses 2016-17 Supervision of Ph.D Thesis Benjamin Diamond; Ph.D thesis title: “Smooth Surfaces in Smooth Fourfolds with Vanishing First Chern Class” (thesis defended in April 2017, JHU) 2011-16 Supervision of Ph.D Thesis Kalina Mincheva; Ph.D thesis title: “Semiring congruences and tropical geometry” (thesis defended in May 2016, JHU) 2010-15 Supervision of Ph.D Thesis JaiUng Jun; Ph.D thesis title: “Algebraic geometry over semistructures and hyperstructures in characteristic one” (thesis defended in May 2015, JHU) 2010-15 Supervision of Ph.D Thesis Jeffrey Tolliver; Ph.D thesis title: “Hyperstructures and idempotent semistructures” (thesis defended in May 2015, JHU) 2010-14 Supervision of Ph.D Thesis Jingjing Zhang 2005-09 Supervision of Ph.D Thesis Abhishek Banerjee; Ph.D thesis title: “Nearby Cycles, Archimedean Complex and Periodicity in Cyclic Homology” (thesis defended in May 2009, JHU) 2003-08 Co-Supervision of Ph.D Thesis (with J. Morava) Susama Agarwala; Ph.D thesis title: “The Geometry of Renormalization” (thesis defended in May 2008, JHU) 2004-08 Supervision of Ph.D Thesis Geoffrey D. Lynch; Ph.D thesis title: “Local Monodromy Operator as an Algebraic Cycle” (thesis defended in November 2008, U. of Toronto). Graduate Teaching (last 10 years) 2018, 2012 Algebra II Second part of a graduate course in abstract algebra (1st year graduate class). Topics: Galois theory, representation theory of finite groups. 2017 Topics in Algebra: Homological Algebra in Nonabelian Cate- gories Description of a theory of homological algebra in semi-exact and homological categories, with particular emphasis for the category of Boolean modules. 2017, 2009 Algebraic Geometry Graduate course on the theory of sheaves and algebraic schemes. 2016 Algebraic Number Theory Graduate course on the theory of the zeta function over global fields of positive characteristic (Hasse-Weil zeta functions). 2012, 2013, 2015, 2010, Algebraic Number Theory 2008, 2007 First part of a graduate course in algebraic number theory (1st year graduate class). Topics: algebraic integers, number fields, Dirichlet’s Theorem on units, cyclotomic fields, local fields, valuations, decomposition and inertia groups, ramification, Riemann-Roch theory. 2015, 2011 Algebraic Geometry Introductory graduate course in algebraic geometry. 2014 Topics in Algebra: Archimedean Cyclic (Co)homology Development of a theory of Archimedean cyclic (co)homology and its appli- cation in the description of the Archimedean local factors of L-functions of arithmetic varieties. 2011 Algebraic Number Theory Class Field Theory 2007 Algebraic Geometry Graduate course on motives of algebraic varities.

Supervision of Undergraduate Theses 2012-13 Supervision of Undergraduate Thesis Sinan Ozdemir; thesis title: “Elliptic Curves, Homomorphic Cryptography and its Applications” (thesis presented in May 2013, JHU)

Teaching at the College (last 10 years) 2018 Honors Algebra II Second part of an advanced course in abstract algebra for the College. Topics: Euclidean, principal, and factorial rings; polynomial rings, Galois theory. 2017, 2011 Honors Linear Algebra Advanced course in linear algebra for the College. 2016, 2012, 2010, 2008 Advanced Algebra I First part of an advanced course in abstract algebra for the College. Topics: groups and rings theory. 2014, 2013 Advanced Algebra II Second part of an advanced course in abstract algebra for the College 2010 Linear Algebra Linear Algebra for the College. 2009 Calculus II Course in analysis for Engineering and Physics. 2008 Calculus I Basic course of analysis for mathematics.

Post-Doctoral Supervision 2008-10 Post-Doctoral Supervision Snigdhayan Mahanta (J.J. Sylvester Assistant Professor, JHU) 2006-09 Post-Doctoral Supervision Eugene Ha (J.J. Sylvester Assistant Professor, JHU).

Inter-University Teaching Activities 2014 Expository talks at “Trimester Program in Noncommutative Geometry and its Applications”, Hausdorff Center for Mathematics HIM, Bonn (Germany). 2010 Expository talks at Masterclass Graduate School, University of Utrecht (Netherland). 2009 Expository talks at School in “Noncommutative Geometry and Operator Algebras”, Vanderbilt University.

Bibliography

1. A. Connes, C. Consani, The Riemann-Roch Strategy, Quantizing the Scaling Site, Preprint (2018). Available at http://arxiv.org/abs/1805.10501 2. A. Connes, C. Consani, Homological Algebra in Characteristic One, Preprint (2017). Sent for publication. Available at https://arxiv.org/abs/1703.02325 3. A. Connes, C. Consani, Geometry of the Scaling Site, Selecta Math. (N.S.) 23 (2017), no. 3, 1803–1850. https://doi.org/10.1007/s00029-017-0313-y Available at http://www.math.jhu.edu/~kc/papers/Selecta2017.pdf. 4. A. Connes, C. Consani, The Scaling Site, C. R. Math. Acad. Sci. Paris 354 (2016), no. 1, 1–6. https://doi.org/10.1016/j.crma.2015.09.027 Available at http://www.math.jhu.edu/~kc/papers/CRAS_2015.pdf. 5. A. Connes, C. Consani, Absolute Algebra and Segal’s Γ-Rings: au Dessou de Spec(Z), J. Number Theory 162 (2016), 518–551. https://doi.org/10.1016/j.jnt.2015.12.002 Available at http://www.math.jhu.edu/~kc/papers/F1_new.pdf. 6. A. Connes, C. Consani, Geometry of the Arithmetic Site, Adv. Math. 291 (2016), 274–329. https://doi.org/10.1016/j.aim.2015.11.045 Available at http://www.math.jhu.edu/~kc/papers/Geometryofthearithmticsite.pdf 7. A. Connes, C. Consani, The Cyclic and Epicyclic Sites, Rend. Semin. Mat. Univ. Padova 134 (2015), 197–237. https://doi/org/10.4171/RSMUP/134-5. Available at http://www.math.jhu.edu/~kc/papers/Thecyclicandepicyclicsites.pdf. 8. A. Connes, C. Consani, The Arithmetic Site, C. R. Math. Acad. Sci. Paris 352 (2014), no. 12, 971–975. https://doi.org/10.1016/j.crma.2014.07.009 Available at http://www.math.jhu.edu/~kc/papers/CRAS_2014.pdf. 9. A. Connes, C. Consani, Projective Geometry in Characteristic One and the Epicyclic Category, Nagoya Math. J. 217 (2015), 95–132. https://doi.org/10.1215/00277630-2887960 Available at http://www.math.jhu.edu/~kc/papers/Epicyclic.pdf. 10. A. Connes, C. Consani, Cyclic Structures and the Topos of Simplicial Sets, J. Pure Appl. Algebra 219 (2015), no. 4, 1211–1235. https://doi.org/10.1016/j.jpaa.2014.06.002 Available at http://www.math.jhu.edu/~kc/papers/Cyclic_structures.pdf. 11. A. Connes, C. Consani, Cyclic Homology, Serre’s Local Factors and the λ-Operations, J. K-Theory 14 (2014), no. 1, 1–45. https://doi.org/10.1017/is014006012jkt270 Available at http://journals.cambridge.org/repo_A93qVXRd. 12. A. Connes, C. Consani, The Universal Thickening of the Field of Real Numbers, Advances in the theory of numbers, 11–74, Fields Inst. Commun., 77, Fields Inst. Res. Math. Sci., Toronto, ON, 2015. https://doi.org/10.1007/978-1-4939-3201-6_2 Available at http://www.math.jhu.edu/~kc/papers/Universalthickening.pdf. 13. A. Connes, C. Consani (Editors), Noncommutative Geometry, Arithmetic, and Related Topics, Proceedings of the Twenty-First Meeting of the Japan-U.S. Mathematics Institute, Johns Hopkins University Press (2012). ISBN: 9781421403526 14. A. Connes, C. Consani On the Arithmetic of the BC-System, J. Noncommut. Geom. 8 (2014), no. 3, 873–945. https://doi.org/10.4171/JNCG/173 Available at http://www.math.jhu.edu/~kc/papers/BC_final.pdf. 15. A. Connes, C. Consani Characteristic One, Entropy and the Absolute Point, Noncommutative geometry, arithmetic, and related topics, 75–139, Johns Hopkins Univ. Press, Baltimore, MD, 2011. ISBN: 9781421403526 Available at http://www.math.jhu.edu/~kc/papers/Jami.pdf 16. A. Connes, C. Consani The Hyperring of Adèle Classes, J. Number Theory 131 (2011), no. 2, 159–194. https://doi.org/10.1016/j.jnt.2010.09.001 Available at http://www.math.jhu.edu/~kc/papers/JNT2.pdf 17. A. Connes, C. Consani Schemes over F1 and Zeta Functions, Compos. Math. 146 (2010), no. 6, 1383–1415. https://doi.org/10.1112/S0010437X09004692. Available at http://www.math.jhu.edu/~kc/papers/Compositio.pdf 18. A. Connes, C. Consani From Monoids to Hyperstructures: in Search of an Absolute Arithmetic, Casimir force, Casimir operators and the Riemann hypothesis, 147–198, Walter de Gruyter, Berlin, 2010. https://doi.org/10.1515/9783110226133.147 Available at http://www.math.jhu.edu/~kc/papers/deGruyer.pdf 19. A. Connes, C. Consani On the Notion of Geometry over F1, J. Algebraic Geom. 20 (2011), no. 3, 525–557. https://doi.org/10.1090/S1056-3911-2010-00535-8 Available at http://www.math.jhu.edu/~kc/papers/JAG.pdf 20. A. Connes, C. Consani, M. Marcolli, The Weil Proof and the Geometry of the Adèles Class Space, Algebra, arithmetic, and geometry: in honor of Yu. I. Manin. Vol. I, 339–405, Progr. Math., 269, Birkhäuser Boston, Inc., Boston, MA, 2009. https://link.springer.com/chapter/10.1007% 2F978-0-8176-4745-2_8 Available at http://www.math.jhu.edu/~kc/papers/Manin_Fest.pdf 21. A. Connes, C. Consani, M. Marcolli, Fun with F1, J. Number Theory 129 (2009), no. 6, 1532–1561. Selected by Elsevier B.V. as “Article of the Future 2011” in Mathematics & Computer Science. https://doi.org/10.1016/j.jnt.2008.08.007 Available at http://www.math.jhu.edu/~kc/papers/JNT1.pdf 22. C. Consani, Noncommutative Geometry and Motives (a quoi Servent les Endomotifs?), Renormal- ization and Galois theories, 1–37, IRMA Lect. Math. Theor. Phys., 15, Eur. Math. Soc., Zürich, 2009. https://doi.org/10.4171/073-1/1 Available at http://www.math.jhu.edu/~kc/papers/CIRM.pdf 23. A. Connes, C. Consani, M. Marcolli, Noncommutative Geometry and Motives: the Thermodynamics of Endomotives, Adv. Math. 214 (2007), no. 2, 761–831. https://doi.org/10.1016/j.aim.2007.03.006 Available at http://www.math.jhu.edu/~kc/papers/Advances.pdf 24. C. Consani, M. Marcolli, Quantum Statistical Mechanics over Function Fields, J. Number Theory 123 (2007), no. 2, 487–528. https://doi.org/10.1016/j.jnt.2006.12.002 Available at http://www.math.jhu.edu/~kc/papers/JNT_withMM.pdf 25. C. Consani, M. Marcolli, Archimedean Cohomology Revisited, Noncommutative geometry and number theory, 109–140, Aspects Math., E37, Friedr. Vieweg, Wiesbaden, 2006. https://doi.org/10.1007/978-3-8348-0352-8_5 Available at http://www.math.jhu.edu/~kc/papers/ArchCoh13.pdf 26. C. Consani, M. Marcolli (Editors), Noncommutative Geometry and Number Theory: Where Arithmetic Meets Geometry and Physics, Aspects of Mathematics E37 Vieweg (2006). ISBN 978-3- 8348-0352-8 27. C. Consani, C. Faber, On the Cusp Form Motives in Genus One and Level One, Moduli spaces and arithmetic geometry, 297–314, Adv. Stud. Pure Math., 45, Math. Soc. Japan, Tokyo, (2006). http://mathsoc.jp/publication/ASPM/aspmlist.html Available at http://www.math.jhu.edu/~kc/papers/APM_withCF.pdf 28. C. Consani, M. Marcolli Non-commutative Geometry, Dynamics and ∞-adic Arakelov Geometry, Selecta Math. (N.S.) 10 (2004), no. 2, 167–251. https://doi.org/10.1007/s00029-004-0369-3. Available at http://www.math.jhu.edu/~kc/papers/Selecta.pdf 29. C. Consani, M. Marcolli, New Perspectives in Arakelov Geometry, Number theory, 81–102, CRM Proc. Lecture Notes, 36, Amer. Math. Soc., Providence, RI, 2004. Electronic ISBN: 978-1-4704-3950- 7. https://doi.org/10.1090/crmp/036 Available at http://www.math.jhu.edu/~kc/papers/CRM.pdf 30. C. Consani, M. Marcolli Spectral triples from Mumford Curves, Int. Math. Res. Not. 2003, no. 36, 1945–1972. https://doi.org/10.1155/S1073792803130954 Available at http://www.math.jhu.edu/~kc/papers/IMRN.pdf 31. C. Consani, M. Marcolli Triplets Spectraux en Géometrie d’Arakelov, C. R. Math. Acad. Sci. Paris 335 (2002), no. 10, 779–784. https://doi.org/10.1016/S1631-073X(02)02569-4 Available at http://www.math.jhu.edu/~kc/papers/CR.pdf 32. C. Consani, M. Kim, The Picard-Lefschetz Formula and a Conjecture of Kato: the Case of Lefschetz Fibrations, Math. Res. Lett. 9 (2002), no. 5–6, 621–631. http://dx.doi.org/\10.4310/MRL.2002.v9.n5.a5 Available at http://www.math.jhu.edu/~kc/papers/MRL.pdf 33. C. Consani, J. Scholten Arithmetic on a Quintic Threefold, Internat. J. Math. 12 (2001), no. 8, 943–972. https://doi.org/10.1142/S0129167X01001118 Available at http://www.math.jhu.edu/~kc/papers/quintic.pdf 34. C. Consani, The Local Monodromy as a Generalized Algebraic Correspondence, With an appendix by Spencer Bloch. Doc. Math. 4 (1999), 65–108. ISSN 1431-0643 (INTERNET). https://www.math.uni-bielefeld.de/documenta/vol-04/03.pdf Available at http://www.math.jhu.edu/~kc/papers/Documenta.pdf 35. C. Consani, Double Complexes and Euler L–Factors, Compositio Math. 111 (1998), no. 3, 323–358. https://doi.org/10.1023/A:1000362027455 Available at http://www.math.jhu.edu/~kc/papers/Compositio1998.pdf 36. C. Consani, Double Complexes and Euler L–Factors on Degenerations of Algebraic Varieties, Thesis (Ph.D.)–The University of Chicago. 1996. 63 pp. Available at http://www.math.jhu.edu/~kc/papers/kthesis.pdf 37. C. Consani, K–Theory of Blow–ups and Vector Bundles on the Cone over a Surface, K-Theory 7 (1993), no. 3, 269–284. https://doi.org/10.1007/BF00961066 Available at http://www.math.jhu.edu/~kc/papers/ktheory.pdf 38. C. Consani, Intersection Theories and K-Theory on Singular Varieties (in italian), Ph.D Thesis at The Universities of Genoa and Turin (1993). 39. C. Consani, A Moving–Lemma for a Singular Variety and Applications to the Grothendieck Group K0(X), Algebraic K-theory, commutative algebra, and algebraic geometry (Santa Margherita Ligure, 1989), 21–45 http://dx.doi.org/10.1090/conm/126