USCDEPARTMENTOFMATHEMATICS • 3620 S. VERMONT AVE, KAP 108 • LOS ANGELES, CA 90089-2532

E - M A I L:[email protected] • W E B: HTTP://SITES.GOOGLE.COM/VIEW/LAUDA-HOME A A R O N D. L A U D A

September 16, 2021

RESEARCHINTERESTS

• Low-dimensional topology and topological quantum field theory • Topological quantum computation • Categorification and its applications • Representation theory of Lie algebras and quantum groups

EDUCATION

2021 Cambridge University Doctor of Science 2006 Cambridge University Ph.D. Mathematics Thesis: Open-closed topological field theory and Khovanov homology, Advisor: Martin Hyland 2003 University of California, Riverside M.S. in Physics Advisor: John Baez 2002 University of California, Riverside B.S in Pure Mathematics, Summa Cum Laude

EMPLOYMENT

February 2019 – present University of Southern California, Los Angeles, CA. Dean’s Leadership Fellow for the Natural Sciences and Mathematics

March 2014 – present University of Southern California, Los Angeles, CA. Professor

November 2013 - March 2014 University of Southern California, Los Angeles, CA. Associate Professor

July 2011 - November 2013 University of Southern California, Los Angeles, CA. Assistant Professor

Fall 2006– Spring 2011 Columbia University, New York, NY. Joseph Fels Ritt Assistant Professor

Fall 2007 Fields Institute, Toronto, Canada. Special Program on ‘Geometric Aspects of Homotopy Theory’ Jerrold E. Marsden Postdoctoral Fellow

1 HONORSAND AWARDS

2021 Doctor of Science, Cambridge University 2019 Fellow of the American Mathematics Society 2016 Mathematical and Physical Sciences Simons Fellow 2014 Section Chair for Seoul ICM Section - Lie Theory and Generalizations 2013 NSF CAREER Award 2011 Alfred P. Sloan Fellowship 2005 Rayleigh-Knight prize, Cambridge University

PUBLICATIONS

Following the convention in mathematics, authors are listed alphabetically. As mathematicians do not work in labs, their independent research career often begins in graduate school, or sooner. The arXiv numbers correspond to the corresponding entries on the ArXiv preprint server, accessible at http://arxiv.org. Graduate students indicated with (∗) and postdocs with (†). 44. Pseudo-Hermitian Levin-Wen models from non-semisimple TQFTs, with Nathan Geer, Bertrand Patureau- Mirand, and Joshua Sussan, (2021), arXiv:2108.10798. 43. A Hermitian TQFT from a non-semisimple category of quantum sl(2)-modules, with Nathan Geer, Bertrand Patureau-Mirand, and Joshua Sussan, (2021), arXiv:2108.09242. 42. Strands algebras and the affine highest weight property for equivariant hypertoric categories, with Anthony Licata and Andy Manion† (2021), arXiv:2107.06480. 41. Super rewriting theory and nondegeneracy of odd categorified sl(2), with Benjamin Dupont*1 and Mark Ebert* (2021), arXiv:2102.00276. 40. From hypertoric geometry to bordered Floer homology via the m = 1 amplituhedron, with Anthony Licata and Andy Manion† (2020), arXiv:2009.03981.

39. An invitation to categorification, with Joshua Sussan, (2021), To appear in the Notices of American Mathematics Society. 38. Braid group actions from categorical symmetric Howe duality on deformed Webster algebras, with Mikhail Khovanov, Joshua Sussan, Yasuyoshi Yonezawa, To appear in Transformation Groups, (2021), arXiv:1802.05358.

37. Ozsvath-Szabo bordered algebras and subquotients of category O, with Andy Manion† Advances in Mathemat- ics, Volume 376, Issue 6, (2021), arXiv:1910.03770. 36. Curved Rickard complexes and link homologies, with Sabin Cautis and Joshua Sussan, Journal für die reine und angewandte Mathematik (Crelle), Volume 2020, Issue 769, 87–119, (2020), doi.org/10.1515/crelle-2019-0044, arXiv:1901.08195. 35. DG structures on odd categorified quantum sl(2), with Ilknur Egilmez*, Quantum Topology, Volume 11, Issue 2, pp. 227–294, (2020), arXiv:1808.04924. 34. Parameters in categorified quantum groups, Algebras and Representation Theory, Volume 23, pp 1265–1284, (2020), arXiv:1812.07654. 33. The Elliptic Hall algebra and the deformed Khovanov Heisenberg category, with Sabin Cautis, Anthony Licata, Peter Samuelson, Joshua Sussan, Selecta Mathematica, (2018), Volume 24, Issue 5, pp 4041-4103, arXiv:1609.03506. 32. W-algebras from Heisenberg categories, with Sabin Cautis, Anthony M. Licata, Joshua Sussan, Journal of the Institute of Mathematics of Jessieu, Volume 17, Issue 5, November (2018) , pp. 981-101,arXiv:1501.00589. 31. A DG-extention of symmetric functions arising from higher representation theory, with Andrea Appel†, Ilknur Egilmez*, and Matthew Hogancamp†, Journal of Combinatorial Algebra, Vol. 2, (2018), No. 2, 169-214, arXiv:1704.00713. 1Benjamin Dupont was a graduate student at Lyon while collaborating on this project.

2 30. The colored HOMFLYPT function is q-holonomic, with Stavros Garoufalidis and Thang T.Q. Lê, Duke Mathe- matics Journal, Volume 167, Number 3 (2018), 397-447. arXiv:1604.08502. 29. Current algebras and categorified quantum groups, with Anna Beliakova, Kazuo Habiro, and Ben Webster, Journal of the London Mathematical Society, Vol. 95, Issue 1, pages 248–276, (2017), arXiv:1412.1417. 28. Trace decategorification of categorified quantum sl(2), with Anna Beliakova, Kazuo Habiro, and Marko Zivkovic*, Mathematische Annalen, Vol. 367, No.1, (2017) pages 397-440, arXiv:1404.1806. 27. An odd categorification of quantum sl(2), with Alex P. Ellis*, Quantum Topology, Vol. 7, No. 2, (2016), pages 329–433, (2016), arXiv:1307.7816. 26. Cyclicity for categorified quantum groups, with Anna Beliakova, Kazuo Habiro, and Ben Webster, Journal of Algebra, Vol. 452, 118-132, (2016), arXiv:1506.04671. 25. Trace decategorification of the Hecke category, with Ben Elias, Journal of Algebra, Vol. 449, 615-634, (2016), arXiv:1504.05267. 24. Khovanov homology is a skew Howe 2-representation of categorified quantum sl(m), with Hoel Queffelec* and David E. V. Rose†, Algebraic and Geometric Topology, Vol. 15, No. 5, 2515–2606, (2015), arXiv:1212.6076. 23. Implicit structure in 2-representations of quantum groups, with Sabin Cautis, Selecta Mathematica , Volume 21, Issue 1, pp 201-244, (2015), arXiv:1111.1431. 22. Trace as an alternative decategorification functor, with Anna Beliakova, Zaur Guliyev*, and Kazuo Habiro, Acta Mathematica Vietnamica, Volume 39, Issue 4, pp 425-480, (2014), arXiv:1409.1198. 21. Oddification of the cohomology of type A Springer varieties, with Heather Russell†, International Mathematics Research Notices, vol. 2014, No. 17 pages 4822-4854, (2014), arXiv:1203.0797. 20. The odd nilHecke algebra and its diagrammatics, with Alexander Ellis* and Mikhail Khovanov, International Mathematics Research Notices, vol. 2014, No. 4, pages 991–1062, (2014), arXiv:1111.1320. 19. Categorified quantum sl(2) is an inverse limit of flag 2-categories, with Anna Beliakova, Transformation Groups, vol. 19, issue 1, pages 1–26, (2014), arXiv:1205.3608. 18. An introduction to diagrammatic algebra and categorified quantum sl(2), Bulletin of the Institute of Mathematics, Academia Sinica, Taipei, Taiwan, vol. 7, no. 2, pp. 165-270, (2012), arXiv:1106.2128. 17. A categorification of the Casimir of quantum sl(2), with Anna Beliakova and Mikhail Khovanov, Advances in Mathematics, 230, No. 3, pages 1442–1501, (2012) arXiv:1008.0370. 16. Extended graphical calculus for categorified quantum sl(2), with Mikhail Khovanov, Marco Mackaay, and Marko Stoši´c, Memoirs of the AMS, 219, (2012), arXiv:0909.1810. 15. Crystals from categorified quantum groups, with Monica Vazirani, Advances in Mathematics, 228, No. 2, pages 803-861, (2011), arXiv:1006.2866. 14. A diagrammatic approach to categorification of quantum groups II, with Mikhail Khovanov, Transactions of the AMS, 363, pages 2685-2700, (2011), arXiv:0804.2080. 13. Categorified quantum sl(2) and equivariant cohomology of iterated flag varieties, Algebras and Representation Theory, 14, No.2 pages 258-282, (2011), arXiv:0803.3848. 12. A pre-history of n-categorical physics, with John Baez, Deep Beauty: Mathematical Innovation and the Search for an Underlying Intelligibility of the Quantum World, pages 13–128, Cambridge Univ. Press, Cambridge, (2011) arXiv:0908.2469. 11. A categorification of quantum sl(2), Advances in Mathematics, 255, No. 6, pages 3327–3424, (2010), arXiv:0803.3652. 10. Crystals from categorified quantum groups, with Monica Vazirani, Discrete Math. Theor. Comput. Sci. Pro- ceedings, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010) pp. 869-880. 9. Categorification in Representation Theory with Anthony Licata and Alistair Savage, Editorial in International Journal of Mathematics and Mathematical Sciences (2010), Article ID 592359. 8. Nilpotency in type A cyclotomic quotients, with Alexander Hoffnung, Journal of Algebraic Combinatorics, 32, No. 4 (2010), 533-555, arXiv:0903.2992.

3 7. A diagrammatic approach to categorification of quantum groups III, with Mikhail Khovanov, Quantum Topology 1, No.1, 1–92, (2010) arXiv:0807.3250. 6. A diagrammatic approach to categorification of quantum groups I, with Mikhail Khovanov, Representation The- ory, 3, 309-347, (2009), arXiv:0803.4121. 5. Open-closed TQFTs extend Khovanov homology from links to tangles, with Hendryk Pfeiffer, Journal of Knot Theory and its Ramifications 18, No.1 (2009) 87–150, arXiv:0606331. 4. Open-closed strings: Two-dimensional extended TQFTs and Frobenius algebras, with Hendryk Pfeiffer, Topol- ogy and its Applications 155 (2008), No. 7, 623–666, arXiv:0510664. 3. State sum construction of two-dimensional open-closed Topological Quantum Field Theories, with Hendryk Pfeiffer, Journal of Knot Theory and its Ramifications 16, No.9 (2007) 1121–1163, arXiv:0602047. 2. Frobenius algebras and ambidextrous adjunctions, Theory and Applications of Categories 16 (2006), No. 4: 84-122, arXiv:0502550. 1. Higher Dimensional Algebra V: 2-Groups, with John Baez, Theory and Applications of Categories 12 (2004): 423 – 491, arXiv:0307200.

BOOKS

• Categorification in Geometry, Topology, and Physics, edited with Anna Beliakova, AMS Contempo- rary Mathematics, Volume: 684, 2017, 267 pages. • Categorification and Higher Representation Theory, edited with Anna Beliakova, AMS Contempo- rary Mathematics, Volume: 683, 2017, 361 pages.

PATENTS AND PATENT APPLICATIONS

• Method and system for encrypting information utilizing three-dimensional shapes, Arthur Parker II Lansing, Solomon Golomb, Aaron Lauda, US Patent No. 20150143113 A1, May 2015.

FUNDING Career-total awarded: US $2,404,182

9. Army Research Office W911NF2010075: Advancing Quantum Information Through Categorification, PI: Aaron Lauda, Award Amount: $799,818, Dates: 05/01/2020-04/30/2024 8. National Science Foundation DMS-1902092: Homotopical Methods in Higher Representation Theory, PI: Aaron Lauda, Award Amount: $235,000, Dates: 07/01/2019-06/30/2022 7. National Science Foundation Focused Research Grant DMS-1664240: FRG: Collaborative Research: Categorifying Quantum Three-Manifold Invariants , Lead PI: Aaron Lauda, Co-PI’s: Sergei Gukov, Mikhail Khovanov, and Raphael Rouquier, Total budget $670,000, (Lauda portion: $147,405.00), Dates: 07/01/17- 06/30/20 6. Mathematics and Physical Sciences-Simons Fellows in Mathematics Award Number: 337963: Col- laboration in Categorification and low-dimensional topology, PI: Aaron Lauda, $98,823, Dates: 01/01/2016 – 12/31/2016. 5. National Science Foundation CAREER Award DMS-1255334: CAREER: Interactions between knot homology and representation theory, PI: Aaron Lauda, Award Amount: $445,000, Dates: 07/01/2013- 06/30/2019 4. John Templeton Foundation Award for Foundational Questions in Science Award Number: 39940: Promoting the principle of categorification in modern scientific thought, PI: Aaron Lauda, Co-PIs: Sabin Cautis, Award Amount: $397,268, Dates: 05/15/2013-05/15/2016

4 3. Fellowship from the Alfred P. Sloan Foundation, PI: Aaron Lauda, Award Amount: $50,000, Dates: 07/01/2011-06/30/2013 2. Zumberge Fund Individual Grant Award: Odd categorification of quantum groups, PI: Aaron Lauda, Award Amount: $25,000, Dates: 07/01/2012-06/30/2013 1. National Science Foundation DMS-0855713: Categorification of quantum groups, PI: Aaron Lauda, Award Amount: $118,657, Dates: 07/01/2009 - 06/30/2012

Conference Grants 3. National Science Foundation Conference grant DMS-1806399 : Topological Quantum Field Theory and Categorification, PI: Aaron Lauda, Co-PI: Mikhail Khovanov, Award Amount: $18,000, Dates: 03/15/2018 – 02/28/2019 2. National Science Foundation Conference grant DMS-1744232 : US-Mexico conference in representa- tion theory and non-commutative algebra , PI: Aaron Lauda, Co-PIs: Milen Yakimov, Award Amount: $19,998.00, Dates: 12/01/2017 – 11/30/2018 1. National Science Foundation Conference grant DMS-1446398 : US-Mexico conference in representa- tion theory and non-commutative algebra , PI: Aaron Lauda, Co-PIs: Milen Yakimov, Award Amount: $49,940.00, Dates: 12/15/2014-11/30/2016

PROFESSIONAL ACTIVITIES

2021 Reviewer for Royal Society Dorothy Hodgkin Fellowship 2017 - Present Editorial Adviser for the the London Mathematical Society, including the Bulletin of the LMS, Journal of LMS, Proceedings of the LMS, and Transactions or the LMS 2016 - Present Editor for the Journal of Pure and Applied Algebra 2017 Editor of two volume edition of AMS Contemporary Mathematics on special issue on “Categorification and Higher Representation Theory" and “Categorification in Geometry, Topology, and Physics". 2015 - 2018 AMS Simons Travel Grants Committee 2010 Editor for International Journal of Mathematics and Mathematical Sciences, special issue on “Categorification in Representation Theory". Available electronically at http://www.hindawi.com/journals/ijmms/2010/si.crt/.

• NSF funding panel member (Multiple years) • NSA Young Investigator grant reviewer (Multiple years) • Assessor for the Australian Research Council (Multiple years) • Reviewer for the Austrian Science Fund (FWF) (Multiple years)

CONFERENCE ORGANIZATION Postdoc participation in conference organization is indicated with (†), current or former graduate student participation is indicated with (∗).

16. Organizer of ICERM Hot Topics Workshop: Foam Evaluation", ICERM, Brown University, November 5–7, 2021. 15. Organizer of “Categorifying quantum 3-manifold invariants Summer School and Workshop", Univer- sity of Southern California, July 16th-22nd, 2018 (with Andy Manion† and Matt Hogancamp†) 14. Organizer of "Categorification and Higher Representation Theory", Institut Mittag-Leffler, Danderyd, Sweeden, 9th July 2018 to 13th June 2018 (with Volodymyr Mazorchuk)

5 13. Organizer of “TQFT and Categorification", Institut d’Etudes Scientifiques de Cargèse, France, April 16th – 20th, 2018 (with Christian Blanchet, Mikhail Khovanov, and Hoel Queffelec∗) 12. Organizer of “Third meeting of th US-Mexico Conference on Representation theory, Categorification, and Noncommutative algebra", Mathematics Institute of UNAM in Mexico City (with Christof Geiss, Daniel Labardini Fragoso, and Milen Yakimov) 11. Organizer of “Quantum topology and categorified representation theory", Isaac Newton Institute, Cambridge, UK, 26th June 2017 to 30th June 2017 (with Anthony Licata) 10. Organizer of “Symmetry in algebra, topology, and physics" as part of the Congress of the Americas, McGill University, Montreal, Canada July 24-28, 2017 (with Nicolas Libedinsky and Joshua Sussan ) 9. Organizer of “Second meeting of th US-Mexico Conference on Representation theory, Categorifica- tion, and Noncommutative algebra" University of Southern California, May 30th-June 3rd, 2016 (with Andrea Appel†, Christof Geiss, and Milen Yakimov) 8. Organizer of “Categorification in Algebra, Geometry and Physics (A conference in honor of the 60th Birthday of Christian Blanchet)", IESC, Menasina, Cargese, France, May 4-8th, 2015 (with Anna Beli- akova and Sabin Cautis). 7. Organizer of “US-Mexico Conference on Representation Theory, Categorification, and Noncommu- tative Algebra" UNAM, Mexico City, January 14th-17th, 2015 (with Milen Yakimov, Christof Geiss, Vladislav Khartchenko). 6. Co-organizer of “Workshop on Categorification and Representation Theory", USC, October 30th-31st, 2014 (with USC post-docs Andrea Appel† and David Rose†). 5. Organizer of “Representation theory and K-theory", University of Southern California in Los Angeles, May 19-22, 2014 (with Aravind Asok, Robert Guralnick, and Susan Montgomery). 4. Organizer of AMS special session “Categorification in representation theory", November 2013 (with David Rose†). 3. Organizer of AMS special session “Link homology and categorification", January 2009 (with Mikhail Khovanov). 2. Organizer of “Introductory Workshop: Homology Theories of Knots and Links", MSRI Berkeley, Jan- uary 25th - 29th, 2010 (with Robert Lipshitz and Dylan Thurston). 1. Organizer of “Categorification on Broadway" graduate student workshop, Columbia University, De- cember 14-15th, 2010.

INVITED LECTURES For a complete list see https://sites.google.com/view/lauda-home/talks Plenary Lectures Plenary Address, The Eighth Pacific Rim Conference in Mathematics, U.C. Berkeley, August 2020 [Canceled - COVID] Plenary speaker, Southeastern Lie Theory conference, North Carolina State University, April 2012 Plenary lecture, QG2 Quantum Geometry and Quantum Gravity Conference, July 2008 Main Speaker, three lectures, Oporto Meeting on Geometry, Topology, and Physics, Portugal, 2010 Plenary lecture, Knots in Washington XXVII, 3rd Japan-USA Workshop in Knot Theory, 2009 Colloquia Physics Department Colloquium, USC, November 16th, 2020 Mathematics Department Colloquium, Ohio State University, February 2020 Mathematics Colloquium, University of Oregon, November 2019 Brandeis-Harvard-MIT-Northeastern Joint Mathematics Colloquium, February 2018 Math Department Colloquium, Columbia University, November 2016 Math Department Colloquium, UCLA, November 2016 Math Department Colloquium, UCR, October 2016 Mathematics Colloquium, Louisiana State University, March 2015

6 Mathematics colloquium, University of Geneva, February 2014 Mathematics colloquium, University of Madison Wisconsin, January 2014 Mathematics colloquium, Temple University, December 2013 Mathematics colloquium, University of Melbourne, October 2013 Algebra Colloquium, East China Normal University, Shanghai, May 2012 Math Colloquium, Georgia Tech, January 2010 LSU Math Colloquium, January 2010 UCSD Math Colloquium, January 2010 Colloquium, Boston College, November 2010 Colloquium, Purdue University, December 10th 2010 Mathematics Colloquium, Nagoya University, January 2009 Mathematics Colloquium, George Washington University, January 2009 Pure Mathematics Colloquiums, University of Sheffield, November 2005 Select Conference Presentations Algebraic and Geometric Categorification, Banff International Research Station for Mathematical Innovation and Dis- covery of Casa Matemà ˛aticaOaxaca , Mexico, December 2019 Quiver Hecke algebra and its applications to topology , Nagoya, Japan, July 2019 Hidden Algebraic Structures in Topology, Caltech, March 2019 Higher symmetries, Aspen Center for Physics, March 2019 Interactions of quantum affine algebras with cluster algebras, current algebras and categorification Catholic University of America, Washington D.C, June 2018 TQFT and Categorification, Institut d’Etudes Scientifiques de Cargese, France, April 2018 Quantum knot homology and supersymmetric gauge theories, Aspen Center for Physics, March 2018 Homological Methods in Algebra and Geometry, AIMS Ghana, August 2016 Diagrammatics and Topology, Okinawa, August 2015 International Congress of Mathematical Physics, Santiago, Chile, July 2015 Categorification in Algebra, Geometry and Physics, IESC, Cargese, France, May 2015 ICM Satellite Conference on Representation Theory and Related Topics, Daegu Korea, August 2014 Quantum Topology, Chelyabinsk, Russia, July 2014 Categorification and geometric representation theory, CRM, Montreal, June 2014 Categorification workshop, Paris 7, December 2013 Physics and Mathematics of Link Homology, Séminaire de Mathématiques Supérieures, Montréal, 2013 Representation theory and categorification, Jiaotong University, Shanghai, China, June 2013 Quantum topology and related topics, Nha Thang, Vietnam, May 2013 Southern California Algebra Conference, UCLA, April 2013 Mapping class groups and categorification, Banff International Research Station, April 2013 German Research Council program in Representation Theory, Bad Boll, Germany, March 2012 Two lectures, Higher Structures in China III, August 2012 Workshop on Category Theoretic Methods in Representation Theory, University of Ottawa, October 2011 Algebraic Lie theory, Cambridge Isaac Newton Institute, Cambridge, UK, September 2011 Swiss Knots 2011, Lake of Thun, Switzerland, May 2011 Taipei Conference on Representation Theory in Academia Sinica, Taipei, Taiwan, December 2010 Algebraic and Combinatorial Approaches to Representation Theory, Indian Institute of Science, Bangalore, August 2010 Double Affine Hecke Algebras and Algebraic Geometry Workshop, MIT, May 2010 Knots in Washington XXIX, George Washington University, December 2009 International workshop on Lie algebras and related topics, NIMS, Daejon, Korea, October 2009 Combinatorial Geometric Structures in Representation Theory, Durham, July 2009 Geometric Representation Theory and Extended Affine Lie Algebras, University of Ottawa, June 2009 Categorification and Geometrisation from Representation Theory University of Glasgow, April 2009 Representation Theory, Geometry & Combinatorics Seminar, Berkeley, October 2008 Select Seminar Invitations

7 Quantum Algebra & Quantum Topology (QAQT) seminar, Ohio State University, February 2020 Mathematical Physics Seminar, UC Berkeley, April 2017 Algebra and Geometry Seminar, Melbourne University, Melbourne Australia, July 2015 Geometry and Topology seminar, Georgia Tech University, April 2015 Algebra seminar, La Spienza University, Rome, March 2014 Algebra and Lie Theory seminar, CU Boulder, November 2012 UCLA Combinatorics seminar, November 2012 Ten lecture series, East China Normal University, Shanghai 2012 Penn State Applied Algebra Seminar, March 2012 L.A. Topology Seminar, November 2011 Southern California Algebraic Geometry seminar, UCLA, November 2011 Two lectures, University Paris Diderot, PPS Seminar, May 2011 Mathematical Physics Seminar, ETH Zurich, 2011 Northeastern GASC seminar, November 2010 UPenn Math/Physics Seminar, October 2010 Rutgers, Lie Groups and Quantum Math Seminar, April 2010 Geometry, Symmetry and Physics seminar, Yale University, February 2010 New York Area Algebra Seminar, CUNY Graduate Center, October 2009 Institute for Mathematics, University of Zurich, July 2009 Algebra and Discrete Mathematics Seminar, University of California Davis, May 2009 Math/Phys Learning Seminar, Stony Brook University, October 2009 Three part lecture series, Kyoto University, Japan, January 2009 Max Planck Institute for Gravitational Physics, Potsdam, December 2005 Topology Seminar, University of Oxford, November 2005 Graduate Lectures and Summer Schools Graduate student seminar, Ohio State University, Ohio State University, February 2020 Three lectures, Introductory Workshop: Higher Categories and Categorification, MSRI, Berkeley, February 2020 Two part introductory lecture, Moab Topology Conference, Moab, Utah. May 2019 Graduate student Colloquium, LSU March 2015 Graduate student topology seminar, LSU, October 2010 Four lectures, Higher Structures 2010, Erwin Schroedinger Institute (ESI), Vienna, October 2010 Introductory workshop: Homology Theories of Knots and Links, MSRI Berkeley, January 2010 Summer School on Link homology, Institute Henri PoincarÃl’, Paris June 2009 Graduate Colloquium, George Washington University, December 2009 Undergraduate Lectures Two-part introductory lecture, Northeastern University, February 2018 Undergraduate Colloquium, LSU, March 2015 REU Colloquium, Cal State Channel Islands, July 2012 Seminars for Undergraduates Too, University of Cambridge Archimedeans, February 2005

GRADUATE STUDENTS

Current students:

• Elif Uskuplu (2nd Year) • Brian Barch(3rd year Physics, co-advisor, primary advisor Paolo Zanardi) • Mark Ebert (4rd year) – Joint paper 41. – Recipient of the Manning Endowed Fellowship 2021.

8 • Namit Anand (5th year Physics, co-advisor, primary advisor Paolo Zanardi) Past students: 7. Nicolle Sandoval Gonzalez (PhD 2019) Dissertation title “Categorical operators and crystal struc- tures on the ring of symmetric functions" • Received the UC President’s Postdoctoral Fellowship at UCLA. • Received Dennis Ray Estes Graduate Research Prize, Department of Mathematics , USC, 2019. • Received Order of Arete, USC This award represents the highest honor accorded graduate students for making notable contributions to the university, academic discipline, community or world at large. 6. Ilknur Egilmez (PhD 2018) Dissertation title "DG Structures on Categorified Quantum Groups" • I have two joint papers 31 and 35 with Egilmez. • Applied Scientist, Amazon 5. Can Ozan Oguz (PhD 2018), Dissertation title "Center and Trace of the Twisted Heisenberg Category" • postdoc at Galatasaray University in ġrstanbul 4. Juan Fernando Valdés Cruz (M.S. 2017), (Masters Student at CIMAT Mexico), Masters Thesis title “Categorification and combinatorics of Schubert polynomials" 3. Laffite Lamberto-Egan (Ph.D 2016), Dissertation title "A categorified braid group action" 2. Mike Abram (PhD 2015), Dissertation title "Symmetries of categorified quantum groups" 1. Amelia Stone (MS 2014) Visiting Students: 1. Hoel Queffelec – visiting graduate student for the Spring 2012 semester from Paris 7 graduated 12/06/2013. • I have one joint paper 24 with Queffelec.

POST-DOCTORALRESEARCHERS

7. Mentor for Anne Dranowski (2021-2023 at USC) 6. Mentor for Andy Manion (2018-2021 at USC) • Manion co-organizing the workshop “CQ3MI Summer School and Workshop", University of Southern California, July 16th-22nd, 2018. • I coauthored publications 37, 40 and 42 with Manion. • Manion accepted a tenure-track position at NC State University during the 2020-2021 COVID hiring cycle. • I mentored Manion’s successful NSF Grant. 5. Mentor for Aaron Mazel Gee (2017- 2020) • 2017 AMS Travel Grant, ($4,000) • USC Zumburge Individual Award ($30,000) • Sherman Fairchild Instructor in Mathematics at Caltech

9 4. Mentor for Matthew Hogancamp (2016-2019 at USC) • I mentored Hogancamp’s successful NSF Grant DMS-1702274. • Hogancamp co-organizing the workshop “CQ3MI Summer School and Workshop", University of Southern California, July 16th-22nd, 2018. • I have published paper 31 with Hogancamp. • Hogancamp accepted a tenure track position at Northeastern University. 3. Co-mentor for Jesse Levitt along with Susan Montgomery (2016 - 2019). 2. Postdoc Mentor for Andrea Appel (NTT Assistant Professor 2013-2017 at USC) • I co-organized a conference “Second meeting of the US-Mexico Conference on Representation theory, Categorification, and Noncommutative Algebra" with Appel at USC, May 30–June 3rd, 2016. • I co-organized a conference “Workshop on Categorification and Representation Theory" with Appel at USC, Oct 30-31st, 2014. • Andrea was awarded a Simons Travel Grant while at USC ($4,000). • I have one published paper 31 with Appel. • Appel accepted a second postdoc at the University of Edinburgh and went on to a tenure track position at the University of Parma. 1. Postdoc Mentor for David Rose (Busemann NTT Assistant Professor 2012-2016 at USC ) . • I mentored Rose’s successful application for a Zumberge Individual Award ($25,000) as the named faculty mentor. • I mentored Rose’s successful NSA Young Investigator Grant ($40,000). • I was the mentor for David Rose’s Simons Travel Grant Award ($4,000). • I have published paper 24 with Rose. • I organized an AMS Sectional Meeting with Rose, November 2-3, 2013 at UCR. We also co- organized a conference “Workshop on Categorification and Representation Theory", USC, Oct 30-31st, 2014. • Rose accepted a tenure track position at the University of North Carolina at Chapel Hill.

PUBLIC OUTREACH

High School Outreach using knot theory (2014): To illustrate the scope with which mathematics can be used, I worked with the students of David Crombecque’s Math 499 course to introduce High school stu- dents from Augustus Hawkins High School to the subject knot theory. Using funding provided by my NSF CAREER award, we brought students to USC for a day of mathematics related events. Together with David Rose, a post doc at USC, we designed a "Knot Matching Game", where students were given various knots and asked to match them with a knot table of all distinct knots. Along the way students were ex- posed to a new type of deductive reasoning as they had to develop primitive knot theoretic tools in order to sort and classify the knots. USC Dornsife wrote an article about this event that contains additional details: http://dornsife.usc.edu/news/stories/1747/knot-a-problem/. YouTube educational videos (2014): with the help of Dornsife productions, I helped produce an introduc- tory video about knot theory designed to give the broad population a new perspective towards modern mathematics. https://www.youtube.com/watch?v=kxaWqKM5JyQ.

EFFORTS TO INCREASE DIVERSITY IN SCIENCE

10 Women in Southern California Research Symposium (2017: I mentored my two female graduate stu- dents, Ilknur Egilmez and Nicolle Sandoval Gonzalez, to help them organize a symposium for women in mathematics in the Southern California area. The principle aim of this symposium is to create a network of women mathematicians in the Southern California area in order to nurture collaborations and provide a conduit for integrated research and educational opportunities. There were 125 participants from Southern California area. The symposium provides a unique opportunity for the PI to mentor his graduate students in both conference organization and in the dissemination of current research developments. African Institute of Mathematical Science (2016): I gave several lectures at an introductory School and Workshop on Homological Methods in Algebra and Geometry, AIMS Ghana, August 2016. US-Mexico Conference (2015–present): I co-organize an annual conference series focusing on non-commutative algebra and categorification. This series began in 2015 in Mexico City and has alternated between the US and Mexico in subsequent years. The US-Mexico conference series aims to strengthen research interaction between the US and Mexico while showcasing prominent Mexican mathematicians to serve as role models to students from underrepresented groups within the US. Young women in topology (2013): I was a plenary speaker for the Young women in topology conference in Bonn, Germany EDGE FIRST Faculty Mentor (2012): Enhancing Diversity in Graduate Education (EDGE) First Year Insti- tute for Research Socialization and Training (FIRST) faculty mentor

SERVICETOTHE DEPARTMENT

• 2021–2022 UCAR Review Committee Chair • COVID 19 - Project Restart Task Force Chair 2020 • New Faculty Mentor 2020 • Department Chair Selection Consultative Committee 2013, 2016. • Panel member and Organizer for Panel Discussion on “Planning your career: questions and advice" for graduate students, USC September 2011, 2013, 2016–2021. • Colloquium Chair 2011–2012, 2012–2013, 2017–2018 academic years. • Graduate Committee 2019–present • Hiring Committee 2014–2021, Chair: 2017, 2019, 2020, 2021 • Merit Committee 2014, 2017. • Geometry/Topology Graduate Committee: Chair F2012, S2012, F2017, S2018, Member: F2011, S2012, F2013, S2014, F2014, F2019. Responsible for writing and grading qualifying exams. • Graduate Research Prize selection committee Spring 2012. • Presented at graduate student orientation representing topology group and organizer of MATH 593 • Mathematics Department Task force on web and communications (Spring 2013–2016). – Improved department website. – Initiated a Math Department Facebook and Twitter feed to more effectively target undergradu- ates and improve access to funding and research opportunities. • Mathematics Department Task force for developing an Undergraduate Math Club (Spring 2013 – 2015).

– Created undergraduate mathematics club at USC. – Hosted and organized events including a welcome BBQ, an invited lecture by UCSD professor Ron Graham, a Career panel, and a final exam study break.

11 – For the 2013-2014 academic year we are expanding to elect math club officers and have a gradu- ate school preparation component.

SERVICETOTHE UNIVERSITY

2020 Tenure-Track and Senior Lateral Dossiers breakout session presenter 2019 – present Dean’s Leadership Fellow in the Natural Sciences & Mathematics 2019 University of Southern California Graduate School Dismissal Appeal Panel 2019 USC Dornsife Project Leap initiative - advisor 2019 Evaluation Committee for faculty led initiatives proposals (White papers and initial reports) - co-chair 2017 – present Dornsife Committee on Appointments, Promotion, and Tenure (DCAPT) 2017 RTPC Promotions committee 2016 Department Chair Selection Consultative Committee 2015 – 2016 Dornsife College Promotions Committee 2014 USC Dornsife 60-second seminars video https://dornsife.usc.edu/60-second-seminars-lauda/ 2014 USC Publicity: I also helped out with USC’s television commercial that was featured on all of USC’s NCAA televised events. 2013 Department Chair Selection Consultative Committee 2013 Panel member for NSF CAREER workshop sponsored by the Center for Excellence in Research 2013 Zumberge Individual Grant program review panel member

12