Min Sha Personal Information Nationality: Chinese Address: School of Mathematics and Statistics University of New South Wales Sydney, NSW 2052, Australia Email: z3496683@ad.unsw.edu.au, shamin2010@gmail.com Phone: +61-(0)93855827 Homepage: http://web.maths.unsw.edu.au/~minsha/ Research Interest Algebraic number theory, Diophantine geometry, algebraic dynamical systems, elliptic curves and their applications, linear recurrence sequences Employment Postdoctoral Fellow University of New South Wales 12/2013 Now (Supervisor: Prof. Igor E. Shparlinski) Education PhD (Number Theory) University of Bordeaux 09/2010 09/2013 Thesis: Topics in Elliptic and Modular Curves Advisor: Prof. Yuri Bilu Date of Defense: 27 September, 2013 Date of Award: 19 September, 2014 Master (Number Theory) Tsinghua University 09/2007 07/2010 Thesis: Galois Groups and Genera of a kind of Quasi-cyclotomic Function Fields Advisor: Prof. Linsheng Yin Bachelor (Mathematics) South China University of Technology 09/2003 07/2007 Thesis: Several New Proofs for Maximum Modulus Principle of Functions of Several Complex Variables Advisor: Prof. Min Wu Awards MQ Research Fellowship 2015, Macquarie University Alain Bensoussan Fellowship 12/2013 12/2014, European Commission (Declined) 1
Outstanding Graduate Award 2010, Tsinghua University (Unique awardee of Department of Mathematical Sciences) 2010, Tsinghua University (Unique awardee of De- Outstanding Master s Thesis Award partment of Mathematical Sciences) Outstanding Bachelor s Thesis Award 2007, South China University of Technology (One of the three awardees of School of Mathematical Sciences) Research Grants p-adic Modular forms and constructions of class fields, 01/2016 12/2018 (with Su Hu and Min-Soo Kim) Funding Agency: National Natural Science Foundation of China Research-in-Pairs Programs and Research Visits 1. Max Planck Institute for Mathematics, Germany (one week) April 2016 (visit Dr. Pieter Moree) 2. Centre International de Rencontres Mathématiques, France (2 weeks) March 2016 (with D. Gomez-Perez) 3. South China University of Technology, China (one week), January 2016 (visited Prof. Su Hu for collaborations) 4. Mittag-Leffler Institute, Sweden (2 weeks) July 2015 (with O. Ahmadi, D. Gomez-Perez and A. Ostafe) 5. Vilnius University, Lithuania (one week), April 2015 (visited Prof. Artūras Dubickas for collaborations) 6. Mathematisches Forschungsinstitut Oberwolfach, Germany (2 weeks) April 2015 (with O. Ahmadi, D. Gomez-Perez and A. Ostafe) 7. South China University of Technology, China (one week), March 2015 (visited Prof. Min Wu for collaborations) 8. Centre International de Rencontres Mathématiques, France (2 weeks) July 2014 (with David Kohel and Igor Shparlinski) Publications 1. Counting dynamical systems over finite fields, Contemporary Mathematics, to appear. (with Alina Ostafe) 2. Corrigendum to On the quantitative dynamical Mordell-Lang conjecture", Journal of Number Theory, 164 (2016), 433 437. (with Alina Ostafe) 2
3. Functional graphs of polynomials over finite fields, Journal of Combinatorial Theory, Series B, 116 (2016), 87 122. (with Sergei V. Konyagin, Florian Luca, Bernard Mans, Luke Mathieson and Igor E. Shparlinski) 4. Positive density of integer polynomials with some prescribed properties, Journal of Number Theory, 159 (2016), 27 44. (with Artūras Dubickas) 5. Lang Trotter and Sato Tate distributions in single and double parametric families of elliptic curves, Acta Arithmetica, 170 (2015), 299 325. (with Igor E. Shparlinski) 6. Explicit form of Cassels p-adic embedding theorem for number fields, Canadian Journal of Mathematics, 67 (2015), 1046 1064. (with Artūras Dubickas and Igor E. Shparlinski) 7. On the quantitative dynamical Mordell-Lang conjecture, Journal of Number Theory, 156 (2015), 161 182. (with Alina Ostafe) 8. Counting and testing dominant polynomials, Experimental Mathematics, 24 (2015), 312 325. (with Artūras Dubickas) 9. On the lattices from elliptic curves over finite fields, Finite Fields and Their Applications, 31 (2015), 84 107. 10. The arithmetic of Carmichael Quotients, Periodica Mathematica Hungarica, 71 (2015), 11 23. 11. Counting degenerate polynomials of fixed degree and bounded height, Monatshefte für Mathematik, 177 (2015), 517 537. (with Artūras Dubickas) 12. On the non-idealness of cyclotomic families of pairing-friendly elliptic curves, Journal of Mathematical Cryptology, 8 (2014), 417 440. 13. Bounding the j-invariant of integral points on certain modular curves, International Journal of Number Theory, 10(6) (2014), 1545 1551. 14. Bounding the j-invariant of integral points on modular curves, International Mathematics Research Notices, 2014(16) (2014), 4492 4520. 15. Bounding the j-invariant of integral points on X + ns(p), Proceedings of the American Mathematical Society, 142 (2014), 3395 3410. (with Aurélien Bajolet) 16. Heuristics of the Cocks-Pinch method, Advances in Mathematics of Communications, 8 (2014), 103 118. 17. Digraphs from Endomorphisms of Finite Cyclic Groups, Journal of Combinatorial Mathematics and Combinatorial Computing, 83 (2012), 105 120. 18. Galois Groups and Genera of a kind of Quasi-cyclotomic Function Fields, Journal of Number Theory, 132 (2012), 2574 2581. (with Linsheng Yin) 19. Monomial dynamical systems of dimension one over finite fields, Acta Arithmetica, 148 (2011), 309 331. (with Su Hu) 20. On the Cycle Structure of Repeated Exponentiation Modulo a Prime Power, Fibonacci Quarterly, 49 (2011), 340 347. 3
Preprints 1. On multiplicatively dependent vectors of algebraic numbers, preprint, 2016. (with Francesco Pappalardi, Igor E. Shparlinski and Cameron Stewart) 2. On two functions arising in the study of Carmichael quotients, preprint, 2016. (with Florian Luca and Igor E. Shparlinski) 3. On distances in lattices from algebraic number fields, preprint, 2016. (with Artūras Dubickas and Igor E. Shparlinski) 4. The Sato Tate distribution in families of elliptic curves with a rational parameter of bounded height, preprint, 2015. (with Igor E. Shparlinski) 5. Gauss factorials of polynomials over finite fields, preprint, 2015. (with Xiumei Li) 6. The Sato Tate distribution in thin parametric families of elliptic curves, preprint, 2015. (with Régis de la Bretèche, Igor E. Shparlinski and José F. Voloch) 7. The arithmetics of consecutive polynomial sequences over finite fields, preprint, 2015. (with Domingo Gómez-Pérez and Alina Ostafe) 8. On the decision problems of linear recurrence sequences, preprint, 2015. 9. Pseudolinearly dependent points on elliptic curves, preprint, 2014. (with Igor E. Shparlinski) In preparations 1. Multiplicative independence of the translations of algebraic numbers. (with Artūras Dubickas) 2. Uniform bounds for linear recurrence sequences over function fields. (with Omran Ahmadi, Domingo Gómez-Pérez, and Alina Ostafe) 3. The average rank of double parametric families of elliptic curves. (with Igor E. Shparlinski) 4. On finding zeros of linear recurrence sequences in intervals. (with Igor E. Shparlinski) 5. Sums of exceptional units in residue class rings of global fields. (with Su Hu) 6. On the elliptic curve y 2 = x(x 2 + p) over certain imaginary quadratic fields. (with Xiumei Li) Talks 1. TBA, Pure Mathematics Seminar, University of New South Wales, May 2016. 2. Counting multiplicatively dependent vectors of algebraic numbers, Max Planck Institute for Mathematics, Bonn, April 2016. 3. Counting multiplicatively dependent vectors of algebraic numbers, South China University of Technology, January 2016. 4
4. Counting dependent vectors over number fields, Pure Mathematics Seminar, University of Melbourne, October 2015. 5. Consecutive polynomial sequences over finite fields, the 59th Annual Meeting of the Australian Mathematical Society, September 2015 6. The Skolem problem of linear recurrence sequences, Vilnius University, April 2015. 7. Some properties of integer polynomials and their applications in linear recurrence sequences, South China University of Technology, March 2015. 8. On the quantitative dynamical Mordell-Lang conjecture, Workshop on Algebraic, Number Theoretic and Graph Theoretic Aspects of Dynamical Systems, Australia, February 2015 9. Lang-Trotter and Sato-Tate conjectures on average for some families of elliptic curves, the 8th Australia New Zealand Mathematics Convention, December 2014. 10. Pseudolinearly dependent points on elliptic curves, Number Theory Down Under, University of Newcastle, October 2014. 11. Effective Cassels p-adic embedding theorem for number fields, UNSW, October 2014. 12. A preferable linear recurrence sequence can be generated randomly, Workshop on Pseudorandomness in Number Theory, CIRM Marseille, July 2014. 13. Effective bounds for integral points on modular curves, Tsinghua University, October 2013. 14. Pairing-friendly elliptic curves, University of Bordeaux, February 2013. Conference organization 1. Workshop on Mathematics in Communications, University of Cantabria, Spain, July 6-8, 2016. Conferences 1. Dynamics and Graphs over Finite Fields: Algebraic, Number Theoretic and Algorithmic Aspects, Marseille, France, March 2016. 2. The 59th Annual Meeting of the Australian Mathematical Society, Flinders University, Australia, September 2015. 3. Number Theory Down Under, University of Newcastle, Australia, September 2015. 4. French-German Summer School Galois Theory and Number Theory, University of Konstanz, Germany, July 2015. 5. Algebraic, Number Theoretic and Graph Theoretic Aspects of Dynamical Systems, UNSW, Sydney, February 2015. 6. The 8th Australia New Zealand Mathematics Convention, University of Melbourne, Australia, December 2014. 7. Number Theory Down Under, University of Newcastle, Australia, October 2014. 5
8. Dynamics and Numbers, Max Planck Institute for Mathematics, Bonn, July 2014. 9. Pseudorandomness in number theory, Centre International de Rencontres Mathématiques, Marseille, July 2014. 10. Thue 150, Institut de Mathématiques de Bordeaux, France, 2013. 11. Sino-French Research Program in Diophantine Geometry, Beijing International Center for Mathematical Research, China, 2012. 12. Galois Representations and Arithmetic Geometry, Institut de Mathématiques de Bordeaux, France, 2012. 13. Galois covers and deformations, Institut de Mathématiques de Bordeaux, France, 2012. 14. Contemporary methods for solving Diophantine equations, Banff International Research Station, Canada, 2012. Professional Service Member of the Australian Mathematical Society. Reviewer of Mathematical Reviews (from 2012). Reviewed articles for the following journals: Ars Combinatoria, Finite Fields and Their Applications, Journal of Algebra and Its Applications, Journal of Algebra, Applicable Algebra (AAECC), International Journal of Number Theory, SIAM Journal on Discrete Mathematics, Proceedings of the American Mathematical Society. Reviewed articles for the following conferences: Fq10, ANTS XI. 6