Office Hours

M 12:30-2pm
Tu 10-10:50am
Th 2:30-3:45pm
And other times as posted in google calendar on my website.

 

interests

  • Number Theory,
  • Abstract Algebra,
  • Algebraic Geometry,
  • Matrix analysis (numerical ranges)
 

Patrick Rault

Associate Professor of

Mathematics

South 326C
1 College Circle
Geneseo, NY 14454
585-245-5392
rault@geneseo.edu

Patrick Rault has been a member of the Geneseo faculty since 2008.

Faculty Information

Education

  • Ph.D, University of Wisconsin at Madison; 2008
  • Delta Certificate in Research, Teaching, and Learning, University of Wisconsin at Madison; 2008
  • B.S, College of William and Mary; 2003
  • Math In Moscow, Independent University of Moscow, Spring 2003
  • Budapest Semesters in Mathematics, Fall 2002
  • Mathematics Advanced Study Semesters, The Pennsylvania State University, Fall 2001

Employment

  • Associate Professor, SUNY College at Geneseo: Fall 2014-
  • Assistant Professor, SUNY College at Geneseo: 2008-2014
  • Teaching Assistant, University of Wisconsin at Madison, 2003-2008
  • VIGRE Fellow, University of Wisconsin at Madison, 2004-2005

Research Interests

Number Theory (counting functions) and Matrix Analysis (numerical ranges).

Publications and Professional Activities

  • Camenga, Kristin; Rault, Patrick X; Sendova, Tsvetanka; Spitkovsky, Ilya. On the Gau–Wu number for some classes of matrices. Linear Algebra and its Applications. 444 (2014), 254-262.
  • Camenga, Kristin; Rault, Patrick X; Rossi, Dan; Sendova, Tsvetanka; Spitkovsky, Ilya. Numerical range of some doubly stochastic matrices. Applied Mathematics and Computation. 221, September 2013, 40 – 47.
  • Rault, Patrick X. On uniform bounds for rational points on rational curves and thin sets of arbitrary degree. Journal of Number Theory. 133 (9), 2013, 3112-3118.
  • Rault, Patrick X; Sendova, Tsvetanka; Spitkovsky, Ilya. 3-by-3 matrices with elliptical numerical range revisited. Electron. J. Linear Algebra 26, 2013, 158-167.
  • Bennett, Mike; Lazebnik, Kirill Y; Rault, Patrick X; Singer, Jeffrey A. On invariant area formulas and lattice point bounds for the intersection of hyperbolic and elliptic regions. Journal of Combinatorics and Number Theory 4 (3), 2012.
  • Cheung, Wilson; Rault, Patrick X. On uniform bounds for rational points on quadratic rational curves and thin sets. Journal of Algebra and Number Theory Academia, August 2012, 37-62.
  • Rault, Patrick X. On uniform bounds for rational points on rational curves and thin sets. JP Journal of Algebra, Number Theory and Applications, 23 (2), 2011, 171—185.
  • Rault, Patrick X. On uniform bounds for lattice points in intersections of hyperbolic plane regions. Journal of Combinatorics and Number Theory. 2 (3), 2010, 209--215
  • Rault, Patrick X. On uniform bounds for rational points on rational curves and thin sets. Ph.D. Thesis, 2008
  • Johnson, Charles R.; Harel, Yonatan; Hillar, Christopher J.; Groves, Jonathan M.; Rault, Patrick X. Absolutely flat idempotents. Electron. J. Linear Algebra 10, 2003, 190—200

Affiliations

  • Elected to the Council on Undergraduate Research (CUR) for 2014-17
  • Center for Undergraduate Research in Mathematics (CURM) $22,000 mini-grant for a 2014-15 student research group.
  • Educational Advancement Foundation (EAF) grant to support training initiatives in Inquiry-Based Learning (IBL). $60,000 for first year. 2014. Joint with St. John Fischer College, Nazareth College, SUNY Plattsburgh, and Buffalo State.
  • Council on Undergraduate Research (CUR) Mathematics and Computer Sciences Division 2013 Faculty Mentoring (National) Award for Outstanding Mentoring of Undergraduate Students in Research.
  • “Honoring Teachers” Award, by the Teaching and Learning Center and the SA Academic Affairs Committee, for “positively impacting students’ experience.” 2013-2014.
  • Project NExT Fellow (New Experiences in Teaching), 2008-2009
  • NSF VIGRE Fellow, 2004-2005
  • Barry M. Goldwater Scholar, 2002-2004
Spring 2015 Classes

MATH 222:
Calculus II

    Derivatives and antiderivatives of the transcendental functions, methods of integration, applications of definite integrals, sequences, improper integrals, and series. Prerequisites: MATH 221. Offered
    every semester
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MATH 319:
Theory of Numbers

    An introduction to classical number theory dealing with such topics as divisibility, prime and composite numbers, Diophantine equations, the congruence notation and its applications, quadratic residue
    s. Prerequisites: MATH 222 and MATH 239. Offered spring, odd years
Read more.