Office Hours

■    M 4-5:30pm.
■    T 11:30am-12:20pm.
■    R 2:30-3:45pm.

 

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
Fall 2014 Classes

MATH 233:
Linear Algebra I

    Study of matrices, matrix operations, and systems of linear equations, with an introduction to vector spaces and linear transformations. Elementary applications of linear algebra are included. Prerequ
    isites: MATH 213 or MATH 221 or permission of instructor. Offered every semester
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MATH 315:
Combinatorics

    As calculus seeks to develop proficiency in analysis problem solving, the aim of this course is to develop proficiency in basic combinatorial problem solving and reasoning. Topics include: Enumeration
    , generating functions, sieve formulas, recurrence relations, graph theory, network analysis, trees, search theory, and block designs. Prerequisites: MATH 222, MATH 233 and either MATH 237 or MATH 239. Offered fall, even years
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