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Accomplishments by Jesse Elliott

2017

Publications:

  • "Idempotent Plethories." Journal of Algebra. Vol. 463 Oct 1, 2016. 33-79. (http://dx.doi.org/10.1016/j.jalgebra.2016.06.008)

2015

Publications:

  • "Semistar Operations on Dedekind Domains." Communications in Algebra. Vol. 43 No. 1 January 2015. 236-248.
  • "Netwon basis relations and applications to integer-valued polynomials and q-binomial coefficients." Integers. Vol. 14 August 2014. 1-22.
  • "Factoring Formal Power Series Over Principal Ideal Domains." Transactions of the American Mathematical Society. Vol. 366 No. 8 May 2014. 3997-4019.
  • "The Probability That Int_n(D) is Free." Commutative Algebra: Recent Advances in Commutative Rings, Integer- Valued Polynomials, and Polynomial Functions. Edited by M. Fontana, S. Glaz, and S. Frisch. New York: Springer-Verlag, 2014. 133-151.

Other Activities:

  • A Dualist Perspective on the Axiom of Constructibility. Conference Talk. Special Session on History and Philosophy of Mathematics, 2015 Spring Eastern Sectional Meeting of the AMS. Georgetown University, Washington, D.C.. Mar 8, 2015.
  • Closure Operations in Commutative Algebra as Quantic Nuclei. Conference talk: Special Session on Closure Operations in Commutative Algebra, 2015 Spring Eastern Sectional Meeting of the AMS. Georgetown University. Washington, D.C.. Mar 8, 2015.
  • Factoring Formal Power Series Over Z. Seminar talk; Algebra/Number Theory/Combinatorics Seminar. Claremont Center for the Mathematical Sciences, Claremont, CA. Sep 30, 2014.
  • Factoring formal power series over Z. Colloquium talk. Mathematics Colloquium, California State University, Chico. Sep 26, 2014.
  • Factoring formal power series over principal ideal domains. Conference talk. 2014 Western Spring Sectional Meeting of the AMS, University of New Mexico. May 5, 2014.

2014

Publications:

  • "Presentations and module bases of integer-valued polynomial rings." Journal of Algebra and Its Applications. Vol. 12 No. 1 January 2013. 1-25.

Other Activities:

  • Newton interpolation, generalized binomial coefficients, and integer-valued polynomials. Conference talk. Commutative Rings, Integer-Valued Polynomials, and Polynomial Functions, Graz, Austria. Dec 20, 2012.

2013

Other Activities:

  • Witt vectors and generalizations. Conference talk. Witt Vectors in Arithmetic, Geometry, and Topology, University of New Mexico. May 15, 2012.
  • Factoring formal power series over principal ideal domains. Conference talk. Fourth International Conference on Mathematical Sciences 2012, Al Ain, United Arab Emirates. Mar 11, 2012.

2012

Publications:

  • "Integer-valued polynomial rings, t-closure, and associated primes." Communications in Algebra. Vol. 39 No. 11 November 2011. 4128-4147.
  • "Birings and plethories of integer-valued polynomials." Third International Meeting on Integer-Valued Polynomials (2010), Actes des Rencontres du CIRM. Vol. 2 No. 2 December 2010. 53-58.

Other Activities:

  • Algebra, number theory, and the philosophy of mathematics. Sabbatical presentation. CSU Channel Islands, Graduate Mathematics Colloquium. Feb 22, 2012.
  • Presentations and regular bases of integer-valued polynomial rings. Talk at Algebra Seminar. Universite' de Picardie Jules Verne. Oct 17, 2011.
  • Introduction to quantales. Talk at Joint Math Meeting of Uni Padova and CSU Channel Islands. Universit`a degli Studi di Padova. Mar 25, 2011.
  • Introduction to integer-valued polynomial rings. Talk at Joint Math Meeting of “Roma Tre” and CSU Channel Islands. Universit`a degli Studi “Roma Tre”. Mar 21, 2011.
  • Quantales and applications to ring theory. Talk at Mathematics Colloquium. San Francisco State University. Mar 2, 2011.
  • "Research in Commutative Algebra and Number Theory." Faculty Development Mini-Grant, CSU Channel Islands. Three units of reassigned time. 2011.
  • "Interdisciplinary Research in the Philosophy of Mathematics to Support Authoring a Text." Sabbatical leave, CSU Channel Islands. one semester paid leave. 2011.

2010

Exhibitions / Presentations:

  • "t-closure and integer-valued polynomial rings." Presented to Algebra Seminar, University of Utah. Salt Lake City, UT. Oct 22, 2010.
  • "Quantales and applications to ring theory." Presented to Mathematics Colloquium, New Mexico State University. Las Cruces, NM. Sep 16, 2010.
  • "t-closure and integer-valued polynomial rings." Presented to Algebra Seminar, New Mexico State University. Las Cruces, NM. Sep 15, 2010.

Publications:

  • "Functorial properties of star operations." Communications in Algebra. Vol. 38 No. 5 Jan 1, 2010. 1466-1490.

Other Activities:

  • "Mathematics, Engineering, Music, Art and Culture of Italy." Instructionally Related Activities Grant, CSU Channel Islands. $25,062. 2011.
  • Biring and plethory structures on integer-valued polynomial rings. Third International Meeting on Integer-Valued Polynomials and Problems in Commutative Algebra. Marseille, France. Nov 29, 2010.
  • Abstract ideal theory, ideal systems, and semistar operations. Rome Commutative Ring Theory Days 2010. Rome, Italy. May 20, 2010.

2009

Exhibitions / Presentations:

  • "Functorial properties of star operations." Presented to 2009 Fall Southeastern Meeting of the American Mathematical Society. Boca Raton, FL. Oct 30, 2009.
  • "Integer-valued polynomial rings and t-linked extensions." Presented to 2008 Fez Conference on Commutative Algebra and Applications. Fez, Morocco. 2008.

Publications:

  • "Some new approaches to integer-valued polynomial rings." Commutative Algebra and its Applications: Proceedings of the Fifth Interational Fez Conference on Commutative Algebra and Applications. Edited by Fontana, Kabbaj, Olberding, and Swanson. New York: de Gruyter, 2009. 223-237.

2008

Publications:

  • "Ring structures on groups of arithmetic functions." Journal of Number Theory. Vol. 128 No. 4 April 2008. 709-730.

2007

Exhibitions / Presentations:

  • "Rings of Integer-Valued Polynomials." Presented to Number Theory Seminar. University of California, Los Angeles. Feb 5, 2008.
  • "Universal Characterizations of Integer-Valued Polynomial Rings." Presented to Abelian Groups and Modules over Commutative Rings. University of Connecticut. Jun 11, 2007.
  • "Integer-Valued Polynomial Rings." Presented to CSUCI and University of Warsaw Joint Math Meeting. University of Warsaw, Poland. May 31, 2007.
  • "Infinity: A Panel Discussion." with R. Christopher, G. Wood, and J. Fogg. Presented to Mathematics Colloquium. CSUCI. May 1, 2007.
  • "Integer-Valued Polynomial Rings." Presented to Mathematics Colloquium. California State University, Dominguez Hills. Apr 11, 2007.

Publications:

  • "Universal properties of integer-valued polynomial rings." Journal of Algebra. Vol. 318 No. 1 December 2007. 68-92.

Other Activities:

  • Reviewer. Mathematical Reviews. 2008.
  • Reviewer. Mathematical Reviews. 2007.

2006

Exhibitions / Presentations:

  • "The Science, Art, and Philosophy of Mathematics." Presented to CSUCI Mathematics Colloquium. California State University Channel Islands. Feb 22, 2007.
  • "Integer-Valued Polynomial Rings." Presented to Claremont Colleges Mathematics Colloquium. Claremont McKenna College, CA. Feb 21, 2007.
  • "A Functorial Approach to Integer-Valued Polynomial Rings." Presented to UCSB Algebra Seminar. UCSB. Nov 13, 2006.
  • "Polynomials in Commutative Algebra." Presented to Centro de Investigacion en Matematicas, Universidad Autonoma del Estado de Hidalgo. Pachuca, Mexico. Mar 24, 2006.

Publications:

  • "Binomial rings, integer-valued polynomials, and lambda-rings." Journal of Pure and Applied Algebra. Vol. 207 No. 1 September 2006. 165-185.
  • "Constructing Witt-Burnside rings." Advances in Mathematics. Vol. 203 2006. 319-363.

Other Activities:

  • "Integer-Valued Polynomial Rings." Faculty Development Mini-Grant, CSUCI. 2007.
  • "Integer-Valued Polynomial Rings." Faculty Development Mini-Grant, CSUCI. 2006.

2004

Exhibitions / Presentations:

  • "Binomial RIngs." Paper delivered at International Symposium on Communative Rings and Monoids. Graz, Austia, September 2004.
  • "Commutative Rings and their Modules." Presented to conference. Cortona, Italy. May 2004.
  • "Introduction to Binomial Rings." Presented to California Lutheran University, California State University Channel Island, and Pepperdine University Mathematics Seminar. February 2004.

Other Activities:

  • "Research in Commutative Algebra and Number Theory." Faculty Development Mini-Grant, California State University Channel Islands. 2004.
  • "Research in Commutative Algebra and Number Theory." Martin V. Smith Faculty Innovation and Excellence Grant, CSUCI. 2004.
  • "Research in Commutative Algebra and Number Theory." Faculty Development Mini-Grant, CSUCI. 2003.