Curriculum Vitae and Publications –Robert Guralnick, September 2020

Name: Robert M. Guralnick

Address: Department of Mathematics University of Southern California Los Angeles, CA 90089-2532

Positions Held:

2022 Rothschild Distinguished Fellow, Newton Institute, Cambridge 2020 Rothschild Distinguished Fellow, Newton Institute, Cambridge 2018 Visitor, Institute for Advanced Study, Princeton 2018 Organizer, Mathematical Sciences Research Institute, Berkeley 2017 Visitor, Institute for Advanced Study, Princeton 2015 Visitor, Institute for Advanced Study, Princeton 2012-3 Visitor, Institute for Advanced Study, Princeton 2012-3 Visiting Fellow, Princeton University 2011 Visitor, Newton Institute, Cambridge 2009 Visiting Fellow, Princeton University 2009 Visiting Fellow, Newton Institute, Cambridge 2009 G. C. Steward Fellow, Gonville & Caius, Cambridge 2008 Visitor, Courant Institute, NYU 2008 Visitor, Institute for Advanced Study, Princeton 2008 Member, Mathematical Sciences Research Institute, Berkeley 2005-6 Member, Institute for Advanced Study, Princeton 2002 Visiting Professor, University of Cambridge 2000 Visiting Member, Institute for Advanced Studies, Hebrew University 1999 Research Professor, Mathematical Sciences Research Institute, Berkeley 1997 Visiting Member, Newton Institute, Cambridge 1996-7 Visiting Member, Mathematical Sciences Research Institute 1990-1996 Chairman, Department of Mathematics, USC 1988- present Professor, USC 1990 Visiting Professor, Institut f¨ur Experimentelle Mathematik, Essen 1989 Visiting Professor, Rutgers 1986 Visiting Associate Professor, Caltech 1985 Visiting Associate Professor, Yale 1983-1988 Associate Professor, USC 1979-1983 Assistant Professor, USC 1977-1979 Bateman Research Instructor, Caltech

Education:

Ph.D. UCLA, 1977 B.A. UCLA, 1973

1 Some Recent Honors and Activities

1. Plenary Speaker, Amitsur Centennial Conference, Jerusalem, 2021 2. Rankin Distinguished Lecturer, University of Glasgow, 2021

3. Chair, Frank Nelson Cole Algebra prize committee, 2020-21 4. Distinguished Editor, Linear Algebra and Applications, 2020- 5. Rothschild Distinguished Fellow, Newton Institute, Cambridge, 2020, 2022

6. Simons Foundation Fellow, 2019–20 7. Plenary Speaker, AMS-Vietnam Meeting, June 2019 8. Clay Plenary Speaker, Groups, Geometry and Representations Conference, Oxford, 2018 9. Frank Nelson Cole prize in Algebra, 2018.

10. Member of the Algebra Selection Committee, International Congress of Mathematicians, 2018 11. Elected Fellow of the American Association for the Advancement of Science, 2017. 12. NSF grants, continuous support, 1983–2024.

13. Invited Speaker, The 20th Midrasha Mathematicae 60 Faces to Groups, Institute for Advanced Studies, Hebrew University, November 2016 14. Distinguished Lecture Series, Center for Mathematical Sciences, Technion, November 2016 15. Plenary Speaker, Geometric and topological aspects of the representation theory of ﬁnite groups, Vancouver, Canada, August 2016

16. Keynote Speaker, Group Actions and Algebraic Combinatorics, Hermonstceux, UK, July 2016 17. Plenary Speaker, Simple groups, representations, and related topics, Cambridge, UK, July 2015 18. Plenary Speaker, Conference on Finite Simple Groups and Related Topics, Warwick, UK, July 2015

19. Hour Speaker, Conference on Zariski Dense Subgroups, IPAM, UCLA, February 2015. 20. Editorial Board, Forum of Mathematics, 2015– ; Managing Editor, November 1, 2015 –. 21. Editorial Board, Bulletin of the AMS, 2015–2023.

22. Invited Speaker, International Congress of Mathematicians, Seoul, Korea, August 2014 23. Member, Review Committee, University of Virginia Math Department, May 2014 24. Plenary Speaker, British Math Colloquium, London, April 2014 25. Distinguished Lecturer, Paciﬁc Institute of Mathematical Sciences, UBC, Vancouver, March 2014

26. Chair, Program Committee, AMS-Israel Joint Meeting, Tel Aviv, June 2014 27. Associate Editor, Annals of Mathematics, 2013–2018 28. Distinguished Editor, LAA, 2020–

2 29. Member, Scientiﬁc Advisory Board, Banﬀ International Research Station, 2013–2017

30. Plenary Lecturer, AMS National Meeting, San Diego, January 2013 31. Simons Foundation Fellow, 2012–13 32. AMS Fellow, 2012–

33. G. C. Steward Fellow, Gonville & Caius College, University of Cambridge, 2009 34. Managing Editor, Transactions and Memoirs of Mathematics, AMS, 2004–2012. 35. Member, Council, AMS, 2004–12 (member Executive Committee, 2004–2008), 2018–2022. 36. Life Fellow, Clare Hall, University of Cambridge, 2000–

37. USC Natural Sciences and Mathematics Division Raubenheimer Award, 1999 (for outstanding contributions in research, teaching and service).

Publications

1. Subﬁelds of algebraically closed ﬁelds (with M. Miller), Math. Mag. 50 (1977), 260-261. 2. On cyclic commutator subgroups (with B. Gordon and M. Miller), Aequationes Math. 17(1978), 241-248.

3. On decomposable commutator subgroups, Glasgow Math. J. 19(1978), 159-162. 4. A remark concerning unipotent matrix groups (with O. Taussky), Linear and Multilinear Algebra 7(1979), 87-89. 5. A note on pairs of matrices with rank one commutator, Linear and Multilinear Algebra 8(1979), 97-99. 6. On a result of Schur, J. Algebra 59(1979), 302-309. 7. Maximal subﬁelds of algebraically closed ﬁelds (with M. Miller), J. Austral. Math. Soc. (A) 29(1980), 462-468.

8. A note on the local global principle for similarity of matrices, Lin. Algebra App. 30(1980), 241-245. 9. Expressing group elements as commutators, Rocky Mountain Math. J. 10(1980), 651-654. 10. On cyclic commutator subgroups, Aequationes Math. 21(1980), 33-38.

11. Triangularization of sets of matrices, Linear and Multilinear Algebra 9(1980), 133-140. 12. Nonexistence of partial traces on nonsolvable groups (with I.M. Isaacs and D.S. Passman), Rocky Mountain Math. J. 11(1981), 235-245. 13. Roth’s theorems and decomposition of modules, Lin. Algebra Appl. 39(1981), 156-165.

14. Similarity of matrices over local rings, Lin. Algebra Appl. 41(1981), 161-174. 15. Isomorphism of modules under ground ring extension, J. Number Theory 14(1982), 307-314. 16. Generation of the lower central series, Glasgow Math. J. 23(1982), 15-20.

3 17. Commutators and commutator subgroups, Advances in Math. 45(1982), 319-330. 18. Module equivalences: Local to global when primitive polynomials represent units (with D. Estes), J. Algebra 77(1982), 138-157. 19. Matrix equivalence and isomorphism of modules, Lin. Algebra Appl. 43(1982), 125-136. 20. Solvable generation of groups and Sylow subgroups of the lower central series (with M. Aschbacher), J. Algebra 77(1982), 189-201. 21. An identity of Schur, Linear and Multilinear Algebra 12(1983), 281-284. 22. Pseudosimilarity and cancellation of modules (with C. Lanski), Lin. Algebra Appl. 47(1982), 111-115. 23. Subgroups of prime power index in a simple group, J. Algebra 81(1983), 304-311. 24. Subgroups inducing the same permutation representation, J. Algebra 81(1983) 312-319. 25. The rank of a commutator (with C. Lanski), Linear and Multilinear Algebra 13(1983), 167-175. 26. Relative Brauer groups of global fields (with B. Fein and M. Schacher) Archiv Der Math. 41(1983), 309-318. 27. The genus of a module, J. Number Theory 18(1984), 169-177. 28. Some applications of the first cohomology group (with M. Aschbacher), J. Algebra 90(1984), 446- 460. 29. Generation of the lower central series II, Glasgow Math. J. 25(1984), 193-201. 30. Equations of prime powers (with D. Estes, M. Schacher, and E. Straus), Pacific J. Math. 118(1985), 359-367. 31. Representations under ring extensions: Latimer-MacDuffee and Taussky correspondences (with D. Estes), Advances in Math. 54(1984), 302-313. 32. Lifting homomorphisms of modules, Illinois J. Math. 29(1985), 153-156. 33. Invariants of finite linear groups on relatively free algebras, Linear Alg. and Appl. 72(1985), 85-92. 34. Subgroups inducing the same permutation representation II (with D. Wales), J. Algebra 96(1985), 94-113. 35. Two generator groups III (with J.L. Brenner and J. Wiegold), Contemp. Math. 33(1984), 82-88. 36. Power cancellation of modules, Pacific J. Math 124 (1986), 131-144. 37. Roth’s theorems for sets of matrices, Linear Alg. and Appl. 71(1985), 113-117. 38. Modules under ground ring extension, p. 150-156 in Order and their Applications edited by I. Reiner and K. Roggenkamp, Lecture Notes in Mathematics, vol. 1142, Springer Verlag, New York, 1984. 39. Generation of simple groups, J. Algebra 103(1986), 381-401. 40. The genus of a module II: Roiter’s theorem, power cancellation and extension of scalars, J. Number Theory 26(1987), 149-165. 41. Projective modules with free multiples and powers (with H. Bass), Proc. AMS 96(1986), 207-208.

4 42. Polynomial rings over Goldie rings are often Goldie (with V. Camillo), Proc. AMS 98(1986), 567-568. 43. The dimension of the ﬁrst cohomology group, p.94 - 97 in Representation Theory II Groups and Orders, edited by V. Dlab, P. Gabriel and G. Michler, Lecture Notes in Mathematics Vol. 1178, Springer Verlag New York, 1985. 44. Torsion in the Picard group and extension of scalars (with H. Bass), J. Pure Applied Algebra 52 (1988), 213-217. 45. Matrices and representations over rings of analytic functions and other one dimensional rings, Mathematics Series, Texas Tech University. Visiting Scholars Lectures 1986-1987, 15(1988), 15- 35.

46. Similarity of holomorphic matrices, Linear Algebra & Appl. 99(1988), 85-96. 47. Presentation of modules when ideals need not be principal (with L. Levy), Illinois J. Math. 32(1988), 593-653. 48. Elementary divisor theorem for noncommutative domains (with L. Levy and C. Odenthal), Proc. Amer. Math. Soc. 104(1988), 1003-1011.

49. Finite groups of genus zero (with J. G. Thompson), J. Algebra 131(1990), 303-341. 50. On the number of generators of a ﬁnite group, Archiv. der Math. 53(1989), 521-523. 51. Zeroes of permutation characters with applications to prime splitting and Brauer groups, J. Algebra 131(1990), 294-302.

52. On abelian quotients of primitive permutation groups (with M. Aschbacher), Proc. AMS 107(1989), 89-95. 53. Normalizing elements of the trace ring of generic matrices (with S. Montgomery), Comm. Algebra 17(1989), 1805-1813.

54. Cancellation counterexamples in Krull dimension 1 (with L. Levy and R. Warfield), Proc. AMS 109(1990), 323-326. 55. Cancellation and direct summands in dimension 1 (with L. Levy), J. Algebra 141(1991) 310 - 347. 56. Galois groups and the multiplicative structure of field extensions (with R. Wiegand), Trans. AMS 331(1992), 563-584. 57. A question of Stafford about affine PI algebras, Comm. Alg. 18(1990), 3055-3057. 58. On the cohomology of alternating and symmetric groups and decomposition of relation modules (with W. Kimmerle), J. Pure and Applied Algebra 69(1990), 135-140.

59. Primitive permutation characters (with J. Saxl), Groups, Combinatorics and Geometry, M. Liebeck and J. Saxl, Ed., LMS LNS 165, Cambridge Univ. Press, Cambridge, 1992, 364-367. 60. The genus of a permutation group, Groups, Combinatorics and Geometry, M. Liebeck and J. Saxl, Ed., LMS LNS 165, Cambridge Univ. Press, Cambridge, 1992, 351-363. 61. Bimodules and automorphisms of noncommutative rings (with S. Montgomery), Trans. AMS, 341 (1994), 917-937. 62. A note on commuting pairs of matrices, Linear and Multilinear Algebra 31(1992), 71-75.

5 63. Similarity of matrices over commutative rings, Linear Algebra and its Applications 157(1991), 55-68. 64. Sylow p-subgroups and subnormal subgroups of ﬁnite groups (with P. Kleidman and R. Lyons), Proc. London Math. Soc., 66(1993), 129-151. 65. A remark on inﬁnite torsion groups with periodic cohomology (with O. Talelli), Comm. in Algebra 20(1992), 1217-1221.

66. Bimodules over pi rings, Methods in Module Theory, G. Abrams, J. Haefner, K. Rangaswama, Eds., Marcel Dekker, 1992, 117-134. 67. Solitary Galois extensions of algebraic number ﬁelds (with L. Stern), J. Number Theory 50 (1995), 1-32.

68. Eigenvalues of symmetric matrices and graphs (with H. Bass and D. Estes), J. Algebra, 168 (1994), 536-567. 69. Probability of generating a classical group, (with W. Kantor and J. Saxl), Communications in Algebra, 22(1994), 1395-1402.

70. Extensions of the Baer-Suzuki theorem (with G. Robinson), Israel J. Math., 82(1993), 281-297. 71. Transitive permutation lattices in the same genus and embeddings of subgroups (with A. Weiss), Contemp. Math., 153(1993), 21-33. 72. Matrices over diﬀerential ﬁelds which commute with their derivative (with W. Adkins and J. C. Evard), Lin. Algebra. & Appl., 190(1993), 253-261.

73. Schur covers and the Carlitz conjecture (with M. Fried. and J. Saxl), Israel J. Math, 82(1993), 157-225. 74. Minimal polynomials of symmetric matrices (with D. Estes), Lin. Algebra. & Appl., 192(1993), 83-99.

75. Invertible preservers of similarity classes, Lin. Algebra. & Appl. 213/213 (1994), 249-257. 76. Multiplicative groups of fields modulo the product of subfields (with J.-L. Colliot-Thélèneand R. Wiegand), Journal Pure and Appl. Algebra 106 (1996), 233–262. 77. Picard groups, cancellation, and the multiplicative structure of fields (with R. Wiegand), Zero- dimensional commutative rings (Knoxville, TN, 1994), 65–79, Lecture Notes in Pure and Appl. Math., 171, Dekker, New York, 1995. 78. The kernel of the map on Picard groups induced by a faithfully flat homomorphism (with D. Jaffe, W. Raskind and R. Wiegand), J. Algebra 183 (1996), 2333–262. 79. One sided normalizing elements (with C. Robson and L. Small), Proc. Amer. Math. Soc. 123 (1995), 1955-1957. 80. Monodromy groups of polynomials (with J. Saxl) in Groups of Lie type and their Geometries, DiMartino and Kantor,eds, Cambridge University Press, 1995, 125-150. 81. Monodromy groups of branched coverings: the generic case (with M. Neubauer), in Recent developments in the inverse Galois problem (Seattle, WA, 1993), 325–352, Contemp. Math., 186, Amer. Math. Soc., Providence, RI, 1995.

6 82. Invertible preservers and algebraic groups II: preservers of similarity invariants and overgroups of PSLn(F ), Linear and Mult. Algebra 43 (1997), 221-255. 83. Invertible preservers and algebraic groups III (with C. K. Li), Linear and Mult. Algebra, 43 (1997), 257 - 282. 84. Bounds for fixed point free elements in a transitive group and applications to curves over finite fields (with D. Wan), Israel J. Math 101 (1997), 255-287. 85. A stable range for quadratic forms over commutative rings (with D. Estes), J. Pure and Applied Algebra 120 (1997), 255-280. 86. Permutability of characters on algebras (with L. Grunenfelder, T. Kosir, H. Radjavi), Pacific J. Math. 178 (1997), 63-70. 87. The Picard group of a certain pullback domain: a non-commutative approach (with R. Wiegand), Commutative ring theory (Fès,1995), 339-347, Lecture Notes in Pure and Appl. Math., 185, Dekker, New York, 1997. 88. Modules for algebraic groups with finitely many orbits on subspaces (with M. Liebeck, D. Macpher- son, G. Seitz), J. Algebra 196 (1997), 211-250. 89. Exceptional polynomials of affine type (with P. Müller), J. Algebra 194 (1997), 429-454. 90. On the minimal degree of a permutation representation (with K. Magaard), J. Algebra, 207 (1998), 127-145. 91. Shirshov’s theorem and representations of semigroups (with A. Freedman, R. Gupta), Pacific J. Math. 178 (1997), 63-70. 92. Linear group with orders having certain large prime divisors (with C. Praeger, T. Pentilla and J. Saxl), Proc. London Math. Soc. 78 (1999), 167–214. 93. Probabilistic generation of simple groups (with W. Kantor), J. Algebra 234 (2000), 743–792. 94. The first cohomology group and generation of simple groups (with C. Hoffman), Proceedings of a Conference on Groups and Geometry, Siena, Trends in Mathematics, 81-90, BirkäuserVerlag, 1998. 95. Genus class groups and separable base change (with R. Wiegand) in Factorization in integral domains, 333-347, Lecture Notes in Pure and Appl. Math., 189, Dekker, New York, 1997. 96. Low dimensional representations of special linear groups in cross characteristics (with P. Tiep), J. London Math. Soc. 78 (1999), 116 - 138. 97. Some applications of subgroup structure to probabilistic generation and covers of curves, Proceed- ings of NATO Algebraic Groups Conference, Cambridge, Kluwer, 1998. 98. Small dimensional representations are semisimple, J. Algebra 220 (1999), 531–541. 99. On p-singular Elements in Chevalley Groups in Characteristic p (with Frank Lübeck), On p- singular elements in Chevalley groups in characteristic p, Groups and computation, III (Columbus, OH, 1999), 169–182, Ohio State Univ. Math. Res. Inst. Publ., 8, de Gruyter, Berlin, 2001. 100. Cyclic quotients of transitive subgroups and extension of constants, J. Algebra 234 (2000), 507–532. 101. The probability of generating a finite soluble group (with J. Wilson), Proc. London Math. Soc. (3) 81 (2000), 405–427.

7 102. Torsion in the genus class groups (with C. Pappacena), Algebra, K-theory, groups, and education (New York, 1997), 47–54, Contemp. Math., 243, Amer. Math. Soc., Providence, RI, 1999. 103. Commuting pairs and triples of matrices and related varieties (with B. A. Sethuraman), Linear Algebra Appl. 310 (2000), 139–148. 104. Supplements in p0 by quasi p-groups an appendix: in Valued fields and covers in characteristic p by David Harbater and Marius van der Put, Fields Inst. Commun., 32, Valuation theory and its applications, Vol. I (Saskatoon, SK, 1999), 175–204, Amer. Math. Soc., Providence, RI, 2002. 105. Appendix in Similarity of the companion matrix and its transpose by Louis Solomon, Special issue dedicated to Hans Schneider, Linear Algebra Appl. 302/303 (1999), 555–561. 106. On the spread of finite simple groups (with A. Shalev), Paul Erdos and his mathematics (Budapest, 1999). Combinatorica 23 (2003), 73–87. 107. Generation of groups by conjugate elements (with J. Saxl), J. Algebra, 268 (2003), 519–571. 108. The rational function analogue of a question of Schur and exceptionality of permutation representations, (with P. Müller,J. Saxl), Mem. Amer. Math. Soc. 162 (2003), no. 773.

109. Biperfect Hopf algebras (with P. Etingof, S. Gelaki and J. Saxl), J. Algebra 232 (2000), 331–335. 110. Random generation of ﬁnite simple groups (with M. W. Liebeck, J. Saxl, Jan; A. Shalev), J. Algebra 219 (1999), no. 1, 345–355. 111. Indecomposable set-theoretical solutions to the quantum Yang-Baxter equation on a set with prime number of elements (with P. Etingof and A. Soloviev), J. Algebra 242 (2001), 709–719.

112. Subgroup growth in some pro-p groups (with Y. Barnea), Proc. Amer. Math. Soc. 130 (2002), 653–659. 113. Derived subgroups of ﬁxed points (with P. Shumyatsky), Israel J. Math. 126 (2001), 345–362.

114. Prescribing ramiﬁcation (with K. Stevenson), in Arithmetic fundamental groups and noncommutative algebra, Proceedings of Symposia in Pure Mathematics, 70 (2002) editors M. Fried and Y. Ihara, 1999 von Neumann Conference on Arithmetic Fundamental Groups and Noncommutative Algebra, August 16-27, 1999 MSRI, 387–406. 115. Genus 0 actions of groups of Lie rank 1 (with D. Frohardt and K. Magaard) in Arithmetic fundamental groups and noncommutative algebra, Proceedings of Symposia in Pure Mathematics, 70 (2002) editors M. Fried and Y. Ihara, 1999 von Neumann Conference on Arithmetic Fundamental Groups and Noncommutative Algebra, August 16-27, 1999 MSRI, 449–484. 116. Cross Characteristic Representations of Symplectic Groups and Unitary Groups (with K. Magaard, J. Saxl, and P. Tiep), J. Algebra 257 (2002), 291–347.

117. Incidence matrices, permutation characters, and the minimal genus of a permutation group (with D. Frohardt and K. Magaard), J. Combin. Theory Ser. A 98 (2002), 87–105. 118. Not all quadrative norms are strongly stable (with M. Goldberg and W. Luxemburg), Indag. Math. (N.S.) 12 (2001), 469–476. 119. Classiﬁcation of 2F-modules, I (with G. Malle), J. Algebra 257 (2002), 348–372.

120. Classiﬁcation of 2F-modules, II (with G. Malle), Finite groups 2003, 117–183, Walter de Gruyter GmbH & Co. KG, Berlin, 2004.

8 121. The 2F-modules for nearly simple groups (with G. Malle and R. Lawther), J. Algebra 307 (2007), 643–676. 122. Rational maps and images of rational points of curves over finite fields, Proceedings of the All Ireland Algebra Days, 2001 (Belfast), Irish Math. Soc. Bull. No. 50 (2002), 71–95. 123. Subgroups of GL which fix sublattices of the subspace lattice (with J. Shareshian), J. Algebra J. Algebra 259 (2003), 147–176.

124. Finite Simple Unisingular Groups of Lie Type (with P. Tiep), J. Group Theory 6 (2003), 271–310. 125. Groups with exactly two subgroups of given order, Comm. Algebra 30 (2002), 4401–4406. 126. Derangements in Simple and Primitive Groups (with J. Fulman), Groups, combinatorics & geometry (Durham, 2001), 99–121, World Sci. Publishing, River Edge, NJ, 2003.

127. Exceptional Polynomials over Arbitrary Fields (with J. Saxl), Algebra, arithmetic and geometry with applications (West Lafayette, IN, 2000), 457–472, Springer, Berlin, 2004. 128. Monodromy groups of coverings of curves, Galois groups and fundamental groups, 1–46, Math. Sci. Res. Inst. Publ., 41, Cambridge Univ. Press, Cambridge, 2003.

129. Cross Characteristic Representations of Even Characteristic Symplectic Groups (with P. Tiep), Trans. Amer. Math. Soc. 356 (2004), 4969–5023. 130. On Orbital Partitions and Exceptionality of Primitive Permutation Groups (with C. Li, C. Praeger, J. Saxl), Trans. Amer. Math. Soc. 356 (2004), 4857–4872.

131. On a question of B. H. Neumann (with I. Pak), Proc. Amer. Math. Soc. 131 (2003), 2021–2025. 132. Stable subnorms. II (with M. Goldberg and W. Luxemburg), Linear Multilinear Algebra 51 (2003), 209–219. 133. Multiplicative maps on invertible matrices that preserve matricial properties (with C. K. Li and L. Rodman), Electron. J. Linear Algebra 10 (2003), 291–319.

134. Reduction theorems for groups of matrices (with J. Bernik and M. Mastank), Linear Algebra Appl. 383 (2004), 119–126. 135. Self-normalizing Sylow subgroups (with G. Malle and G. Navarro), Proc. Amer. Math. Soc. 132 (2004), 973–979.

136. Conjugacy class properties of the extension of GL(n, q) generated by the inverse transpose involu- tion (with J. Fulman), J. Algebra 275 (2004), 356–396. 137. Larsen’s conjecture and decomposition of tensor products (with P. Tiep), Represent. Theory 9 (2005), 138–208.

138. Inequalities for ﬁnite group permutation modules (with D. Goldstein and M. Isaacs), Trans. Amer. Math. Soc. 357 (2005), 4017–4042. 139. Symmetric and Alternating Groups as Monodromy Groups of Riemann Surfaces I: Generic Covers and Covers with Many Branch Points (with J. Shareshian), Memoirs Amer. Math. Soc. 2007 (189), No. 886, 128 pp.

140. Thompson-like characterizations of the solvable radical (with B. Kunyavskii, E. Plotkin and A. Shalev), J. Algebra 300 (2006), 363–375.

9 141. Weakly closed unipotent subgroups in Chevalley groups (with G. Röhlre),J. Algebra 300 (2006), 729–740. 142. On the commuting probability in finite groups (with G. Robinson), J. Algebra 300 (2006), 509–528. 143. The direct product theorem for profinite groups (with D. Goldstein), J. Group Theory 9 (2006), 317–322.

144. A question about Pic(X) as a G-module (with D. Goldstein and D. Joyner), Computational aspects of algebraic curves, 232–242, Lecture Notes Ser. Comput., 13, World Sci. Publ., Hackensack, NJ, 2005. 145. The non-coprime k(GV ) problem (with P. Tiep), J. Algebra 293 (2005), 185–242.

146. Irreducible polynomials which are locally reducible everywhere (with M. Schacher and J. Sonn), Proc. Amer. Math. Soc. 133 (2005), 3171–3177. 147. Automorphisms of the modular curve (with P. Bending and A. Camina), Progress in Galois theory, 25–37, Dev. Math., 12, Springer, New York, 2005. 148. Orders of ﬁnite groups of matrices (with M. Lorenz), Groups, rings and algebras, 141–161, Con- temp. Math., 420, Amer. Math. Soc., Providence, RI, 2006. 149. Alternating forms and self-adjoint operators (with D. Goldstein), J. Algebra 308 (2007), 330–349. 150. Inversion invariant additive subgroups of division rings (with D. Goldstein, L. Small and E. Zel- manov), Paciﬁc J. Math. 227 (2006), 287–294.

151. Permutation polytopes and indecomposable elements in permutation groups (with D. Perkinson), J. Combin. Theory Ser. A 113 (2006), 1243–1256. 152. Intersections of conjugacy classes and subgroups of algebraic groups, Proc. Amer. Math. Soc. 135 (2007), 689–693.

153. Sets of elements that pairwise generate a linear group (with J. Britnell, A. Evseev, P. Holmes, A. Maróti),J. Combin. Theory Ser. A 115 (2008), 442–465. 154. Presentations of finite simple groups: a quantitative approach, (with W. Kantor, M. Kassabov and A. Lubotzky), J. Amer. Math. Soc. 21 (2008), 711–774. 155. Presentations of finite simple groups: a cohomological and profinite approach (with W. Kantor, M. Kassabov and A. Lubotzky), Groups, Geometry and Dynamics, Groups Geom. Dyn. 1 (2007), 469–523. 156. Presentations of finite simple groups: a computational approach (with W. Kantor, M. Kassabov and A. Lubotzky), J. Eur. Math. Soc. 13 (2011), 39–458.

157. Exceptional covers and bijections on rational points (with T. Tucker and M. Zieve), Int. Math. Res. Not. IMRN 2007, no. 1, Art. ID rnm004, 20 pp. 158. Frobenius-Schur indicators for subgroups and the Drinfel’d double of Weyl groups (with S. Mont- gomery), Trans. Amer. Math. Soc. 361 (2009), 3611–3632. 159. Frobenius groups as monodromy groups, J. Aust. Math. Soc. 85 (2008), 191–196.

160. Elementary abelian 2-subgroups of Sidki type in ﬁnite groups (with M. Aschbacher and Y. Segev), Groups Geom. Dyn. 1 (2007), 347–400.

10 161. Oort groups and lifting problems (with T. Chinburg and D. Harbater), Composito Math., 114 (2008), 849–866. 162. On fixed points of permutations (with P. Diaconis and J. Fulman), J. Algebraic Comb. 28 (2008), 189–218. 163. Characteristic polynomials of automorphisms of hyperelliptic curves (with E. Howe), Arithmetic, geometry, cryptography and coding theory, 101–111, Contemp. Math., 487, Amer. Math. Soc., Providence, RI, 2009. 164. Proficient finite groups, (with W. Kantor, M. Kassabov and A. Lubotzky), J. Algebra 326 (2011), 169–184. 165. Nonisomorphic curves that become isomorphic over extensions of coprime degrees (with D. Gold- stein, E. Howe and M. Zieve), J. Algebra, 320 (2008), 2526–2558. 166. Symmetric powers and conjectures of Kollárand Larsen (with Tiep), Inventiones Math., 174 (2008), 505–554. 167. Polynomials with PSL(2) Monodromy (with M. Zieve), Ann. of Math. (2) 172 (2010), 1315–1359. 168. A new family of exceptional polynomials in characteristic 2 (with J. Rosenberg and M. Zieve), Ann. of Math. (2) 172 (2010), 1361–1390. 169. Bounds on the number and sizes of conjugacy classes in finite Chevalley groups with applications to derangements(with J. Fulman), Trans. Amer. Math. Soc. 364 (2012), 3023–3070. 170. Base sizes for symmetric groups (with T. Burness and J. Saxl), Bull. Lond. Math. Soc. 43 (2011), 386–391. 171. Frobenius subgroups of free profinite products (with D. Haran), Bull. Lond. Math. Soc. 43 (2011), no. 3, 467–477. 172. Commutators and wreath products. Character theory of finite groups, 79-82, Contemp. Math., 524, Amer. Math. Soc., Providence, RI, 2010. 173. Automorphic realization of residual Galois representations (with N. Katz and M. Harris), J. Eu- ropean Math. Soc, 12 (2010), 915–937. 174. First cohomology group of Chevalley groups in cross characteristic (with P. Tiep), Annals Math., 174 ( 2011), 543–559. 175. Characterizations of the solvable radical (with P. Flavell and S. Guest), Proc. Amer. Math. Soc. 138 (2010), 1161–1170. 176. Hamiltonian cycles in the generating graphs of finite groups (with T. Breuer, A. Lucchini, A. Maróti,G. Nagy). Bull. Lond. Math. Soc. 42 (2010), 621–633. 177. Nil subrings of endomorphism rings of finitely generated modules over affine PI-rings (with L. Small and E. Zelmanov), J. Algebra 324 (2010), 3044–3047. 178. Real class sizes and real character degrees (with G. Navarro and P. Tiep), Math. Proc. Cambridge Philos. Soc. 150 (2011), 47–71. 179. On a subfactor generalization of Wall’s conjecture (with F. Xu), J. Algebra 332 (2011), 457–468, 180. Average dimension of fixed point spaces with applications (with A. Maroti), Advances Math. 226 (2011), 298–308.

11 181. The local lifting problem for actions of finite groups on curves (with T. Chinburg and D. Harbater), Ann. Sci. Ec.´ Norm. Supér44, fascicule 4 (2011). 182. A new solvability criterion for finite groups (with S. Dolfi, M. Herzog and C. Praeger), J. London Math. Soc. 85 (2012), 269–281. 183. Products of conjugacy classes and fixed point spaces (with G. Malle), J. Amer. Math. Soc. 25 (2012), 77–121.

184. A problem of Koll´arand Larsen on ﬁnite linear groups and crepant resolutions (with P. Tiep), J. European Math. Soc. 14 (2012), 605–657. 185. Simple groups admit Beauville structures (with G. Malle), J. Lond. Math. Soc. (2) 85 (2012), 694–721.

186. Strongly dense free subgroups of semisimple algebraic groups (with E. Breuillard, B. Green and T. Tao), Israel J. Math, 192 (2012), 347–379. 187. Representation growth in positive characteristic and conjugacy classes of maximal subgroups (with M. Larsen and P. Tiep), Duke Math. J. 161 (2012), 107–137.

188. Adequate subgroups (with F. Herzig, R. Taylor and J. Thorne), J. Inst. Math. Jussieu 11 (2012), no. 4, 907–920. 189. Adequate subgroups II, Bull. Math. Sciences 2 (2012), 193–203. 190. Coprime subdegrees for primitive permutation groups and completely reducible linear groups, (with S. Dolﬁ, C. Praeger and P. Spiga), Israel J. Math. 195 (2013), 745-772.

191. Low degree representations of simple Lie groups (with M. Larsen and C. Manack), Proc. Amer. Math. Soc. 140 (2012), 1823–1834. 192. The automorphism groups of a family of maximal curves (with B. Malmskog and R. Pries), J. Algebra 361 (2012), 92–106.

193. Certain subgroups of Weyl groups are split (with D. Goldstein), New trends in noncommutative algebra, 10–113, Contemp. Math., 562, Amer. Math. Soc., Providence, RI, 2012. 194. Characteristic polynomials and ﬁxed spaces of semisimple elements (with G. Malle), Recent developments in Lie algebras, groups and representation theory, 173–186, Proc. Sympos. Pure Math., 86, Amer. Math. Soc., Providence, RI, 2012.

195. Products of conjugacy classes in ﬁnite and algebraic simple groups (with G. Malle and P. Tiep), Adv. Math. 234 (2013), 618–652. 196. On the non-coprime k(GV )-problem (with A. Maroti), J. Algebra 385 (2013), 80–101. 197. Base sizes for S-actions of ﬁnite classical groups (with T. Burness and J. Saxl), Israel J. Math. 199 (2014), no. 2, 711–756.

198. Rational rigidity for E8(p) (with G. Malle). Compos. Math. 150 (2014), 1679–1702. 199. Lifting in Frattini covers and a characterization of ﬁnite solvable groups (with P. Tiep), J. Reine Angew. Math. 708 (2015), 49–72.

200. Cosets of Sylow subgroups and a conjecture of Richard Taylor (with D. Goldstein), J. Algebra 398 (2014), 569–573.

12 201. Groups with exactly one irreducible character of degree divisible by p (with D. Goldstein, M. Lewis, A. Moretó,G. Navarro and P. Tiep), Algebra Number Theory 8 (2014), no. 2, 397–428. 202. Regular semisimple classes (with J. Fulman), Linear Algebra Appl. 439 (2013), no. 2, 488–503. 203. Bass units as free factors in integral group rings of simple groups (with J. Goncalves and A. del Rio), J. Algebra 404 (2014), 100–123. 204. Primitive monodromy groups of genus at most two (with D. Frohardt, K. Magaard), J. Algebra 417 (2014), 234–274. 205. Products and commutators of classes in algebraic groups (with G. Malle), Math. Ann. 362 (2015), 743–771. 206. Variations on the Baer-Suzuki Theorem (with G. Malle), Math. Z. 279 (2015), 981–1006. 207. Applications of the classification of finite simple groups, Proceedings of the International Congress of Mathematicians, Seoul 2014, Vol. II, 163–177, KYUNG MOON SA Co., Ltd, Seoul. 208. Expansion in finite groups of Lie type (with E. Breuillard, B. Green and T. Tao), J. Eur. Math. Soc. 17 (2015), 1367–1434. 209. Effective results on the Waring problem for finite simple groups (with P. Tiep), Amer. J. Math. 137 (2015), 1401–1430. 210. Derangements in Subspace Actions of Finite Classical Groups (with J. Fulman), Trans. Amer. Math. Soc. 369 (2017), 2521–2572. 211. On the maximal number of coprime subdegrees in finite primitive permutation groups (with S. Dolfi, C. Praeger and P. Spiga), Israel J. Math. 216 (2016), 107–147. 212. Simple algebraic stabilizing polynomials (with S. Garibaldi), Forum Math. Pi 3 (2015), e3, 41 pp. 213. Base size for algebraic groups (with T. Burness and J. Saxl), J. Eur. Math. Soc. (JEMS) 19 (2017), 2269–2341. 214. Adequate groups of low degree (with F. Herzig and P. Tiep), Algebra Number Theory 9 (2015), 77–147. 215. Adequate subgroups and indecomposable modules (with F. Herzig and P. Tiep), J. Eur. Math. Soc. (JEMS) 19 (2017), 1231–1291. 216. Conjugacy classes of derangements in finite transitive groups, Trudy (Proceedings) of the Steklov Institute (MIAN), Tr. Mat. Inst. Steklova 292 (2016), Algebra, Geometriya i Teoriya Chisel, 118–123. 217. On rational and concise words (with P. Shumyatsky) J. Algebra 429 (2015), 213–217. 218. On a relation between the rank and the proportion of derangements in finite transitive permutation groups (with I. M. Isaacs and P. Spiga), J. Combin. Theory Ser. A 136 (2015), 198–200. 219. Squaring a conjugacy class and cosets of normal subgroups (with G. Navarro), Proc. Amer. Math. Soc. 144 (2016), 1939–1945. 220. Finite groups with odd Sylow normalizers (with G. Navarro and P. Tiep), Proc. Amer. Math. Soc. 144 (2016), 5129–5139. 221. Essential dimension of algebraic groups, including bad characteristic (with S. Garibaldi), Arch. Math. (Basel) 107 (2016), 101–119.

13 222. Spinors and essential dimension (with S. Garibaldi and an appendix by A. Premet), Compos. Math. 153 (2017), 535–556.

223. Rational Rigidity for F4(p) (with F. L¨ubeck and J. Yu), Adv. Math. 302 (2016), 48–58. 224. A lower bound for the dimension of a highest weight module (with D. Goldstein and R. Stong), Represent. Theory 21 (2017), 611–625.

225. Derangements in ﬁnite classical groups for actions related to extension ﬁeld and imprimitive subgroups and the solution of the Boston-Shalev conjecture (with J. Fulman), Trans. Amer. Math. Soc. 370 (2018), 4601–4622. 226. Global Oort groups (with T. Chinburg and D. Harbater, J. Algebra 473 (2017), 374–396.

227. Normalizers of primitive permutation groups (with A. Maro´ti and L. Pyber), Adv. Math. 310 (2017), 1017–1063. 228. Asymptotics for the number of involutions in classical groups (with J. Fulman and D. Stanton), J. Group Theory 20 (2017), 871–902. 229. Globally Irreducible Weyl Modules (with S, Garibaldi and D. Nakano), J. Algebra 477 (2017), 69–87. 230. Endomorphism fields of abelian varieties (with K. Kedlaya), Res. Number Theory 3 (2017), Art. 22. 231. Globally Irreducible Weyl Modules for Quantum Groups (with S, Garibaldi and D. Nakano), Geometric and topological aspects of the representation theory of finite groups, 313–326, Springer Proc. Math. Stat., 242, Springer, Cham, 2018. 232. Enumeration of commuting pairs in Lie algebras over finite fields (with J. Fulman), Ann. Comb. 22 (2018), 295– 316. 233. On isometry groups of self-adjoint traceless and skew-symmetric matrices (with M. Gaál),Linear Algebra Appl. 541 (2018), 211–220. 234. Symmetric and alternating powers of Weil representations of finite symplectic groups (with K. Magaard and P. Tiep), Bull. Inst. Math. Acad. Sinica, New Series 13 (2018), 443–461. 235. Surjective word maps and Burnside’s paqb theorem (with M. Liebeck, E. O’Brien, A. Shalev, and P. Tiep), Invent. Math. 213 (2018), 589–695. 236. Rigid local systems and alternating groups (with N. Katz and P. Tiep), Tunis. J. Math. 1 (2019), 295–320. 237. Permutation representations of nonsplit extensions involving alternating groups (with M. Liebeck), Israel J. Math. 229 (2019), 181–191.

238. Conjugacy classes, characters and products of elements (with A. Moretó),Math. Nachr. 292 (2019), 1315–1320. 239. Zero one generation laws for finite simple groups (with M. Liebeck, F. Lübeck and A. Shalev), Proc. Amer. Math. Soc. 147 (2019), 2331–2347.

240. On a primitive action of G2 (with T. Burness), Appendix A in On the minimal dimension of a ﬁnite simple group (by T. Burness, M. Garzoni and A. Lucchini), J. Combin. Theory Ser. A 171 (2020).

14 241. Cohomology and sectional rank (with P. Tiep), J. Algebra 558 (2020), 434–452.

242. Variants of some of the Brauer-Fowler theorems (with G. Robinson), J. Algebra 558 (2020), 453– 484. 243. On the singular value decomposition over ﬁnite ﬁelds and orbits of GU × GU, Indag. Math., to appear.

244. A note on abelian subgroups of maximal order (with S. Alvazidis), Rend. Lincei Mat. Appl. 31 (2020), 31–334. 245. Cohomology and sectional rank II (with P. Tiep), preprint. 246. Centers of Sylow subgroups and automorphisms (with G. Glauberman, J. Lynd and G. Navarro), Israel J. Math. 240 (2020), no. 1, 253–266. 247. Character levels and character bounds (with M. Larsen and P. Tiep), Forum of Mathematics, Pi (2020), Vol. 8, e2, 81 pages. 248. Character levels and character bounds II (with M. Larsen and P. Tiep), submitted.

249. Generically free representations I: large representations (with S. Garibaldi), Algebra & Number Theory 14 (2020), no. 6, 1577–1611. 250. Generically free representations II: irreducible representations (with S. Garibaldi), Transform. Groups 25 (2020), no. 3, 793–817. 251. Generically free representations III: exceptionally bad characteristic (with S. Garibaldi), Trans- form. Groups 25 (2020), no. 3, 819–841. 252. Simple Lie groups stabilizing G-invariant norms (wth M. Ga´al),Linear Algebra Appl. 609 (2021), 308–316. 253. Almost simple monodromy groups of genus at most two with six or more branch points (with D. Frohardt, C. Hoﬀman and K. Magaard), preprint. 254. Generic stabilizers in actions of simple algebraic groups (with R. Lawther), arXiv:1904.13375 and arXiv:1904.13382 submitted to Memoirs Amer. Math. Soc. (300 pages). 255. Topological generation of exceptional algebraic groups (with T. Burness and S. Gerhardt), Adv. Math. 369 (2020), 107177, 50 pp.

256. On the generalized Fitting height and insoluble length of ﬁnite groups (with G. Tracey), Bull. Lond. Math. Soc. 52 (2020), no. 5, 924–931. 257. The spread of a ﬁnite group (with T. Burness and S. Harper), Ann. of Math. (2) 193 (2021), 619–687.

258. Coprime automorphisms of ﬁnite groups (with Cristina Acciarri and Pavel Shumyatsky), Trans. Amer. Math. Soc., to appear. 259. Real constituents of permutation characters (with G. Navarro), J. Algebra, to appear. 260. Commuting involutions and elementary abelian subgroups of simple groups (with G. Robinson), J. Algebra, to appear. 261. Finite groups can be generated by a π-subgroup and a π0-subgroup (with T. Breuer), arXiv:2103.17216.

15 262. Generic stabilizers for simple algebraic groups (with S. Garibaldi), submitted, arXiv:2105.09486.

263. Topological generation of simple algebraic groups (with T. Burness and S. Gerhardt), submitted, arXiv:2108.06592. 264. Strongly dense free subgroups of semisimple algebraic groups II (with E. Breuillard and M. Larsen), preprint.

265. Strongly dense free subgroups of semisimple algebraic groups III (with E. Breuillard and M. Larsen), preprint.

16 Some Invited Conferences and Lectures

1. Taussky’s Work in Linear Algebra, Taussky Memorial Conference, Caltech, April 1996. 2. Finite Orbit Modules for Algebraic Groups, Representation Meeting, Heidelberg, Germany, August 1996. 3. Olga Taussky – Jack Todd Lecture, Annual International Linear Algebra Society Meeting, Chem- nitz, Germany, August 1996. 4. Exceptional Polynomials, Groups and Geometry, Siena, Italy, September 1996.

5. Rational functions and elliptic curves, Oberwolfach, May 1997 6. Rational functions and elliptic curves, London Algebra Seminar, May 1997. 7. Generating simple groups by conjugates, Birmingham Colloquium, May 1997. 8. Applications of subgroup structure, Newton Institute Conference on Algebraic Groups, June 1997.

9. Bass and (linear) Algebra, Conference in Honor of Hyman Bass, Columbia University, November 1997. 10. Coverings of generic Riemann surfaces, IP Lecture on Galois Theory, UCI , January 1998. 11. Small representations are semisimple, University of Chicago Group Theory Seminar, April 1998.

12. Small representations are semisimple, Oberwolfach, December 1998. 13. Rational functions and elliptic curves, University of Chicago Group Theory Seminar, April 1999. 14. Curves and Groups, MSRI-Evans Lecture, Berkeley, September 1999.

15. Probabilistic Methods in Generation of Finite Groups, UCSC Colloquium, September 1999. 16. Small genus representations of groups and generic covers, Workshop on Galois Groups and Fun- damental Groups, MSRI, October 1999. 17. Permutation Groups and Curves, Conference on Finite Simple Groups, Bad Honnef, Germany, February 2000.

18. Kuwait Lecture, Cambridge University, Permutation Groups and Curves, February 2000. 19. Low Dimensional Representations, Cambridge University Algebra Seminar, February 2000. 20. Permutation Groups and Curves, University of Warwick Colloquium, February 2000.

21. Low Dimensional Representations, MSRI Noncommutative Algebra Seminar, March 2000. 22. Permutation Groups and Coverings of Curve (3 lectures), Conference on Finite Simple Groups and Computational Group Theory, Milan, May 2000. 23. Generation of Finite and Algebraic Groups, Conference on Algebraic Groups, Milan, May 2000.

24. Generation of Finite Groups, Conference on Asymptotic Group Theory, Hebrew University, Jerusalem, May 2000. 25. All Ireland Algebra Days, Dublin, May 2001.

17 26. Luminy Conference on Galois Groups, June 2001. 27. Durham Conference on Groups, Combinatorics and Geometries, Durham, UK, July 2001. 28. University of Pennsylvania Algebra Seminar, May 2002. 29. Princeton University Algebraic Geometry Seminar, May 2002. 30. Oberwolfach Meeting on Arithmetic and Differential Galois Groups, July 2002. 31. Oberwolfach Meeting on Groups and Geometries, September 2002. 32. Main Speaker, Conference in Honor of John Thompson’s 70th Birthday, Cambridge, September 2002. 33. Main Speaker, Galois Group Conference, University of Florida, November 2002. 34. Special Lecture on Math History, University of Florida, November 2002. 35. UCI Algebra Seminar, Automorphism Groups of Curves, November 2002. 36. UC Berkeley Group Theory Seminar, Derangements and Probabilistic Generation, December 2002. 37. Main Speaker, Group Theory Meeting, On the k(GV ) problem in non coprime characteristic, University of Florida, March 2003. 38. Colloquium, Low dimensional representations of finite groups, Temple University, May 2003. 39. Colloquium, Automorphism groups of curves, University of Pennsylvania, May 2003. 40. Main Speaker, Probability and Groups Conference, Derangements in permutation groups, Bu- dapest, July 2003. 41. Workshop on Arithmetic Galois Theory, Banff, September 2003. 42. Colloquium, Exceptional Polynomials, Stanford University, October 2003. 43. Group Theory Conference, Yale University, New Haven, October 2003. 44. Plenary Speaker, Low Dimensional Representations of Finite Groups, ILAS Conference, Coimbra, Portugal, July 2004. 45. Colloquium, Automorphism Groups of Curves, University of Wisconsin, October 2004. 46. Algebraic Geometry Seminar, UC Berkeley, Generation of finite and algebraic groups, February 2005. 47. Plenary Speaker, Mappings from the generic curve, Wiegandfest, Lincoln, Nebraska, May 2005. 48. Colloquium, Low Dimensional Representations, Temple University, October 2005. 49. Plenary Speaker, Canadian Math. Soc. Annual Meeting, Probabilistic generation of simple groups, Vancouver, December 2005. 50. Probabilistic Generation of Finite Simple Groups, SCAC, UCLA, March 2006. 51. Presentations of finite simple groups and cohomology, Oberwolfach, March 2006. 52. Member’s Seminar, IAS, Princeton, Probabilistic Generation of Finite Simple Groups, April 2006. 53. Number Theory Seminar, IAS, Princeton, Maps from the Generic Curve of Genus g, May 2006.

18 54. Presentations of finite simple groups, Hebrew University, May 2006. 55. Applications of representation theory (2 talks), Conference on Group Representations and Com- binatorics, Gainesville Sept. 2007 56. Presentations of finite simple groups, Group Theory Day, Tucson, Oct. 2007, 57. AMS Special Session on Representation Theory, AMS National Meeting, San Diego, Jan. 2008. 58. Maps from the generic curve, UC Berkeley Number Theory Seminar, April 2008. 59. Generators and relations for finite groups, UC Davis Discrete Math Seminar, April 2008. 60. Derangements, Colorado State Colloquium, Colorado Colloquium September 2008. 61. Derangements, University of Colorado Colloquium, September 2008. 62. Exceptional polynomials, University of Arizona seminar, October 2008. 63. Derangements, Southwest Group Theory Conference, Tucson, November 2008. 64. Bijective rational maps, UCLA Number Theory Seminar, November 2008. 65. Presentations and cohomology, Cambridge Algebra Seminar, May 2009. 66. Presentations and cohomology, Imperial College, London, May 2009. 67. Permutation groups and covering of curves, Conference in Honor of John Thompson, Newton Institute, May 2009. 68. Presentations and cohomology, Conference in Honor of Alex Zalesski, Milan, May 2009. 69. On a theorem of Cebatorev, Conference in Honor of Marty Isaacs, Valencia, Spain June 2009. 70. Derangements in finite and algebraic groups, ALT workshop, Newton Insitute, June 2009. 71. Applications of permutation groups, Berlin Summer School on Finite and Algebraic Groups, Berlin, September 2009. 72. Presentations and cohomology, Penn Algebra Seminar, Philadelphia, October 2009. 73. Presentations and cohomology, Georgia Algebra Seminar, Athens, October 2009. 74. Exceptional polynomials, Ohio State Colloquium, Columbus, October 2009. 75. Fixed point spaces, AMS Special Session, UCLA, October 2010. 76. Fixed point spaces of linear groups, Southwest Group Theory Conference, November 2010. 77. Expanders and words, AMS Special Session, New Orleans, Jan. 2011 78. Some remarks on the future of mathematical publishing, MSRI Workshop on Mathematical Pub- lishing, February 2011, Berkeley. 79. Dimensions of fixed point spaces, Southeast Lie Theory Conference (in honor of Len Scott), Uni- versity of Virginia, May 2011. 80. A generalization of Burnside’s Theorem, Caltech Number Theory Seminar, June 2011. 81. Expanders and generation of simple finite and algebraic groups, Groups and Additive Combina- torics, Newton Institute Satellite Meeting, Wales, June 2011.

19 82. Authorship and other issues in mathematical publishing, Committee on Publication Ethics Work- shop, UCSD, San Diego, October 2011. 83. Maps from the generic Riemann surface, Topology Seminar, Graduate Center, CUNY, October 2011. 84. Base size for algebraic groups, Southwest Group Theory Conference, Tucson, November 2011.

85. Unipotent classes in algebraic groups, Special Session, AMS Annual Meeting, Boston, January 2012. 86. A generalization of Burnside’s Theorem, Wisconsin Number Theory Seminar, April 2012. 87. Maps from the generic Riemann surface, Wisconsin Colloquium, April 2012.

88. Expanders and generation of simple finite groups, Words and Growth, Midrasha 2012, Hebrew University, June 2012. 89. Lifting and characterizations of finite solvable groups, Amitsur Seminar, Tel Aviv, June 2012. 90. Maximal subgroups of finite groups, Groups and Geometry, Banff, September 2012.

91. E8(p) is a Galois group over Q, Harvard Number Theory Seminar, November 2012. 92. Strongly Dense Subgroups, Stonybrook Colloquium, November 2012. 93. Strongly Dense Subgroups, Penn Algebra Seminar, December 2012. 94. Generation and presentation of ﬁnite groups, Invited Hour Talk, AMS annual meeting, San Diego, January 2013.

95. E8(p) is a Galois group over Q, Yale Colloquium, January 2013. 96. Derangements in Finite Groups, Princeton Colloquium, February 2013. 97. Strongly Dense Subgroups, New York Group Theory Seminar, September 2014.

98. Dimension of ﬁxed spaces, Yale Algebra Seminar, September 2014. 99. Dimension of ﬁxed spaces, Rutgers Algebra Seminar, October 2014. 100. PIMS Distinguished Lecturer, UBC, Vancouver, March 2014.

101. Plenary Speaker, British Mathematics Colloquium, April 2014. 102. Invited Speaker, International Congress of Mathematics, Seoul, August 2014. 103. Hour Speaker, Conference on Zariski Dense Subgroups, IPAM, UCLA, February 2015. 104. Plenary Speaker, Conference on Finite Simple Groups and Related Topics, Warwick, UK, July 2015 105. Plenary Speaker, Simple groups, representations, and related topics, Cambridge, UK, July 2015 106. Keynote Speaker, Group Actions and Algebraic Combinatorics, Hailsham, UK, July 2016 107. Plenary Speaker, Geometric and topological aspects of the representation theory of ﬁnite groups, Vancouver, Canada, August 2016 108. Invited Speaker, Algebra Extravaganza, Temple University, July 2017.

20 Grants, Prizes and Other Activities

1. Rothschild Distinguished Fellow, Newton Institute, Cambridge, 2020. 2. Simons Foundation Fellowship, 2020. 3. Plenary Speaker, AMS-Vietnam Meeting, June 2019. 4. Frank Nelson Cole prize in Algebra, 2018. 5. Member of the Algebra Selection Committee, International Congress of Mathematicians, 2018 6. Elected Fellow of the American Association for the Advancement of Science, 2017. 7. Member, Council of the AMS, 2005-13, 2017-21. 8. Editorial Board, Forum of Mathematics, 2015–; Mangaging Editor, November 1, 2015 –. 9. BSF grant (with D. Neftin and M. Zieve), 2015–2019. 10. Simons Foundation Fellowship, 2012-2013. 11. Fellow of the AMS, 2012 – 12. G. C. Steward Fellow, Gonville & Caius College, Cambridge University, 2009. 13. USC Natural Sciences and Mathematics Division Raubenheimer Award, 1999 (for outstanding contributions in research, teaching and service). 14. Member, Scientiﬁc Advisory Board, BIRS, 2013–2018. 15. NSF Grants 1984 - 2022. 16. NSF FRG Grant, 2013–2016. 17. Chair, Program Committee, AMS-Israel Joint Meeting, Tel Aviv, June 2014. 18. NATO Grant (with J. Saxl), 1994 - 1998. 19. EPSERC Grant (with J. Saxl), 2002 - 2005. 20. Life Fellow, Clare Hall, University of Cambridge, 2000– present. 21. Editorial Board, Transactions and Memoirs of the AMS, 2003 – 2013. 22. Managing Editor, Transactions and Memoirs of the AMS, 2005-2013. 23. Associate Editor, Annals of Mathematics, 2013–present. 24. Member, Executive Committee of the AMS council, 2005-2009. 25. Member, Long Range Planning Committee, AMS, 2006-2008. 26. Co-organizer, Conference for John Conway, Princeton, November 2015. 27. Chair, Program Committee, AMS-Israel Joint meeting, July 2014. 28. Co-organizer, Conference for G. Robinson’s 60th Birthday, Aberdeen, September 2013. 29. Co-organizer, Conference of John Thompson’s 80th Birthday, Cambridge, September 2012. 30. Organizer, Banﬀ workshop on permutation groups, July 2013.

21 31. Co-organizer, AIM meeting on Cohomology, June 2012.

32. Organizer, Banﬀ workshop on permutation groups, July 2009. 33. Chair, Organizing Committee, Conference on Hopf Algebras and Related Topics (in honor of Susan Montgomery), supported by NSF, Feb. 2009. 34. Organizer, Oberwolfach workshop on permutation groups, July 2008.

35. Chair, Organizing Committee, Conference in honor of Persi Diaconis’ 60th birthday, UCSD, Jan- uary 2004. 36. Co-organizer, Conference on Applications of Simple Groups and Computational Group Theory, Milan, May 2000.

37. Member, Committee on AMS Mathematical Surveys and Monographs, 2013–2022, Chair, 2018-22. 38. Member, AMS Committee on University Lecture Series, 2013–2021. 39. Editor, Springer Book Series, Developments in Mathematics, 2009–2012. 40. Editorial Board, Paciﬁc Journal of Mathematics, 1997– 2003.

41. Board of Governors, Paciﬁc Journal of Mathematics, 1997–present. 42. Editor, Communications in Algebra, 1989 – 1999. 43. Associate Editor, Linear Algebra and its Applications, 1985 – 2006.

44. Senior Editor, Linear Algebra and its Applications, 2007–present 45. Member, Editorial Board, Linear and Multilinear Algebra, 1993– 2008. 46. Editor, Journal of Group Theory, 2002 – present. 47. Editor, Electronic Journal of Linear Algebra, 2002 – 2013.

48. Editor, Quaestiones Mathematicae, 2003 – 2011. 49. Editor for Special Volume of Journal of Algebra for Robert Steinberg 80th Birthday, 2002. 50. Editor for Special Volume of Journal of Algebra for Kay Magaard memorial, 2019-2020.

51. National Security Agency Grant Proposals Board, 1998 - 1999, 2001 - 2003. 52. CDRF Panel (NSF grants to FSU scientists), 2001–2 53. Scientiﬁc Committee, ILAS 2005 meeting. 54. Taussky-Todd Speaker Selection Committee, ILAS 2004 meeting.

55. Committee of Visitors, NSF, February 1997. 56. Member, Focus Committee for Center for Communications Research, 1999–2002 (chair, 2001-2). 57. Member, AMS Subcommittee on Fellows, 2002.

58. Organizing Committee for Von Neumann Symposium, MSRI, August 1999. 59. Group theory advisor, www.arXiv.org, 2002 - present.

22 60. Member (Chair, 2002–2004), Focus Advisory Board, Center for Communications Research, 2001 - 2004. 61. Vigre External Review Committee, University of California, Berkeley, March 2002. 62. Vigre External Review Committee, University of Texas, March 2003. 63. Member, Scientiﬁc Organizing Committee, ILAS Meeting, Regina, Canada, July 2006. 64. Reviewer, Math Reviews and Zentralblatt 65. NSF Group Theory Panel, February 2004 66. NSF Algebra Panel, January 2005, December 2006 67. NSF Career Grant Panel, October 2006 68. NSF Representation Theory Panel, Jan. 2011, Jan. 2019 69. 2005 Hans Schneider Prize Committee 70. Member, NSF Postdoc Panel, 2004 71. Speaker, IMMERSE Program for incoming graduate students, University of Nebraska, Lincoln, July 2005. 72. Member, Outside Review Committee, CSUDH Mathematics Department, February 2007. 73. Member, Georgia VIGRE review committee, October 2009. 74. Chair, AMS Book Committee, Monographs, 2014–2022. 75. Member, AMS Book Committee, Survey, 2015–2023. 76. Member, AMS Council, 2019–2022.

Ph. D. Students Michael Neubauer 1989 Professor, California State University, Northridge Randall Allen 1995 Chris Pappacena 1998 NSA Mathematician Corenliu Hoﬀman 1998 Birmingham, Retired Yong Han 2007 Samsung, Korea Joseph DiMuro 2008 Biola College Simon Guest 2008 Goldman & Sachs, London Andrei Pavelescu 2012 University of South Alabama Spencer Gebhardt 2017 USC Matthew Donner 2018 Eilidh McKemmie 2019 Jerusalem, Rutgers

Postdoctoral Advisees Gerhard R¨ohrle 1990-2 Professor, Universit¨atBochum Ray Ross 1991-3 Michael Zieve 1998-9 Michigan Yiftach Barnea 1999 (MSRI) Royal Holloway, UK Attila Maroti 2004–2008 Budapest Andrea Jedwab 2010-2011 Jay Taylor 2019-21 Manchester

23 Some University and Department Service

1. Chair, Department of Mathematics, 1990–6. 2. Member, Committee on Excellence in Graduate Programs, 1994. 3. Member, College Faculty Handbook Committee, 1994.

4. Chair, Departmental Search Committee, 1997–9. 5. Section Head, Core Math Section, 1997–9. 6. Member, LAS Personnel Committee, Social Sciences, 1997-9 7. Chair, LAS Personnel Committee, NS & M, 2001-3

8. Member, University Faculty Senate, 1997-9, 2001-2. 9. Chair, Departmental Merit Committee, 2001–4 (Chair, 2002–4). 10. Member, LAS Faculty Council, 1997-9, 2001-4, 2011-3.

11. Member, University Committee on Faculty Tenure and Privileges, 1997-2007. 12. Member, LAS Email Retention Committee, 2003. 13. Member, Raubenheimer Selection Committee, 2004. 14. Member, College Graduate Curriculum Committee, 2006–7.

15. Chair, Search Committee, 2006–8 16. Associate Chair, 2007 17. Member, Merit Committee 2009-12, 18. Chair, Chair Consultative Committee, 2010.

19. Chair, Merit Committee, 2013, 2017 20. Chair, Search Committee, 2014 21. Member, Merit Committee, 2015, 2018

22. Member, Search Committee, 2015–16 23. Chair Search Committee, 2018, 2020