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Talks

Invited Talks:

  • Stratifications on moduli spaces of curves and superelliptic loci, MCAG 2013, Michigan Computational Algebraic Geometry, Western Michigan University, Kalamazoo, May 3-4, 2013
  • Vanishing theta-nulls of algebraic curves with automorphisms, SIAM Conference, Raleigh, NC, Oct. 6-8, 2011. 
  • MSRI, Hybrid Methodologies for Symbolic-Numeric Computation, November 2010,
  • NATO ASI, Opatija, Croatia, 2010: 
    Genus 2 curves and their applications to cryptography
  • Algebraic curves of small genus and their automorphisms,  University of Delaware, March 2008. 
  • Genus 2 curves covering elliptic curves, Simon Fraser University, Oct. 2007.
  • Remarks on some old problems of algebraic geometry, Michigan Tech. University, Sep. 2007
  • A historical view of theta functions, University of Lublin, Poland, May 2007. 
  • Theta functions and automorphism groups of curves, Galoistheorie Kolloquium, Institut fur Experimentelle Mathematik (IEM), Essen, Germany, 2006. 
  • Genus 2 curves with (5, 5) split Jacobian, Institute for Experimental Mathematics, Essen, December 2004.
  • Conference in Computational Algebra and Cryptography,  University of Florida, March 2003.
  • Galois Theory Conference, In honor of J. Thompson 70-th birthday.  University of Florida,  Nov 4-8,  2002
  • Problems in computational algebraic geometry, Colloquium, University of Florida, September 2001
  • Genus 2 curves covering elliptic curves, Workshop on Arithmetic Geometry, MSRI, Berkeley, Dec. 2000.
  • Modular curves and Hurwitz spaces, Conference on Topological Groups, TU-Munchen,June 2000. 
  • Curves of genus two with (n,n)-decomposable Jacobians, AG Gruppentheorie, Erlangen, March 2000. 
  • Explicit equation of certain Hurwitz spaces, University of Heidelberg, Germany, May 1999.


All talks:


2015
  • Julia quadratic of superelliptic Riemann surfaces,  AMS Special Session on Riemann surfaces and their automorphisms, Chicago, Oct. 3-4, 2015.
We will give a brief review of how to algebraically determine the Julia quadratic of superelliptic Riemann surfaces.  Computations for surfaces of genus 2 and 3 will be shown.  Moreover, we will compare such computations with the case when the superelliptic surface has extra automorphisms.
 
  • Theta functions and symmetric weight enumerators for codes over imaginary quadratic fields,
    AMS Special Session on Coding Theory, Chicago, Oct. 3-4, 2015.

  • Integral minimal models for binary forms, Department of Mathematics, Number theory Seminar,
    University of Florida, Gainesville, June 25, 2015.

  • Binary forms of minimal height, AMS Sectional Meeting, East Lansing, March 14, 2015
2014
  • Heights of algebraic curves, NATO ASI, Ohrid, Macedonia

2013
Abstract:  For a fixed genus $g>1$ we discuss the stratification of the moduli space $\mathcal M_g$ based on the automorphism groups of the curves. Then for each superelliptic locus of $\mathcal M_g$ we define the corresponding dihedral invariants and give a stratification of the corresponding moduli in terms of these invariants. Decomposition of the superelliptic Jacobians will be determined for all 1 < g < 10 and an algorithm is provided for all g.
Abstract: For a fixed genus $g>1$ we discuss the stratification of the moduli space $\mathcal M_g$ based on the automorphism groups of the curves. Then for each superelliptic locus of $\mathcal M_g$ we define the corresponding dihedral invariants and give a stratification of the corresponding moduli in terms of these invariants. If time permits, decomposition of the corresponding superelliptic Jacobians will be discussed.
  • Automorphisms of curves and their Jacobians,  AMS Special Session on on Computational Advances on Special Functions and Tropical Geometry, Iowa State University, April 2013.
Abstract:  We will show an explicit way of describing the hyperelliptic moduli of genus 3 and its 3-dimensional sublocus of curves with extra involutions.  Then, if time permits we will go over some arithmetic applications about genus three hyperelliptic curves with many rational points.  The talk will be accessible to a general audience.  
                 

2012
  • An explicit description of the hyperelliptic moduli of genus 3, Department of Mathematics Colloquium, Michigan Tech, Nov. 2012
  • Some remarks on binary octavics, Department of Mathematics Colloquium, Clevaland State University, Nov. 2012
  • An introduction to the invariant theory of binary forms, Duquesne University, October 2012.
  • Plenary talk, Some remarks on theta functions and their applications, Conference on Applications of Algebra, Istanbul, Turkey, June 2012.
  • Thetanulls of algebraic curves and some applications, AMS Special session on Computational  Algebraic Geometry, Tampa, Florida, March 2012.
  • Interesting families of algebraic curves, Mathematics of Computation, AMS National Meeting,  Boston, Jan. 2012.
2011
  • Half-integer theta-nulls of superelliptic curves, AMS Sectional Meeting, Salt Lake City, Oct.  22-23, 2011.
  • Theta Functions of algebraic curves, Special Session on theta functions, SIAM Conference, Raleigh, Oct. 6-8. 2011.
  • Computational aspects of low genus curves, Laurier Centennial Conference: AMMCS-2011,  Waterloo, July 2011.
  • Theta-nulls of algebraic curves, 10th Panhellenic Geometry Conference, Patras, Geece, May  27-29, 2011,
2010
2009
  • Second Workshop on Mathematical Cryptology, Santander, Spain, October 22-25, 2009.
2008
  • Some remarks on thetanulls of algebraic curves, NATO ASI, Vlora, Albania, May ??, 2008
  • Algebraic curves of small genus and their automorphisms, Discrete Math Colloquium, University of Delaware, March 2008. 
2007
  • Genus 2 curves covering elliptic curves, Simon Fraser University, Oct. 2007. 
  • Equations of curves with automorphisms, AMS Special session, DePaul University, Oct. 2007. 
  • Some historical remarks on automorphisms of algebraic curves, Department of Mathematics and Statistics, Colloquium, Oakland University, Oct. 2007. 
  • Remarks on some old problems of algebraic geometry, Michigan Tech. University, Sep. 2007 
  • Moduli spaces of curves and theta functions, Vlora conference in Algebra, Coding Theory, and Cryptography, Vlora, Albania, May 26-27, 2007. 
  • A historical view of theta functions, University of Lublin, Poland, May 2007. 
  • Theta functions and algebraic curves with automorphisms, Algebra Seminar, Wayne State University, February 7, 2007. 
2006
  • Theta functions and algebraic curves, Math Colloquium, Oakland University, Fall 2006. 
  • Codes over rings of size four, lattices, and their theta functions, University of Lublin, Poland, Fall 2006. 
  • Some open problems in computational geometry, University of Michigan-Dearborn, Fall 2006. 
  • Theta functions and automorphism groups of curves, Galoistheorie Kolloquium, Institut fur Experimentelle Mathematik (IEM), Essen, Germany, 2006. 
  • Theta functions and application to coding theory, ACA 2006, Varna, Bulgaria, 2006. 
  • Invariants of binary forms, Math Colloquium, Oakland University, Winter 2006. 
2005
  • Algebraic curves and their applications in engineering, Sigma-Chi society, Oakland Univ. Fall 2005. 
  • Algebraic varieties associated to network coding, Wayne State University, Fall 2005.
  • Hyperelliptic curves with reduced automorphism group A5 , AMS Western section, Santa Barbara,April 2005.
  • Genus 2 curves that admit a degree 5 map to an elliptic curve, Joint AMS meeting, Atlanta, January 2005.
2004
  • Genus 2 curves with (5, 5) split Jacobian, Institute for Experimental Mathematics, Essen, Germany, December 2004.
  • Field of moduli of curves, a computational approach, Workshop Computational Arithmetic Geometry, PIMS SFU, July 5 - 9, 2004.
  • On the field of moduli of curves, Algebra seminar, Wayne State University, April 2004.
2003
  • Genus 2 curves with degree 5 elliptic subcovers, 991-14-21 AMS, Southeastern Section Meeting,Chapel Hill, October 2003. 
  • Determining the automorphism group of algebraic curves, ISSAC 03, Drexler University, Philadelphia, August 2003. 
  • Computational aspects of hyperelliptic curves, ACA 03, Raleigh, NC, July 2003. 
  • The monodromy group of a generic curve covering P1 , Joint International Meeting of AMS and RSME, Seville, Spain, June 2003. 
  • Computational aspects of hyperelliptic curves, University of Cantabria, Santander, Spain, June 2003. 
  • Loci of hyperel liptic curves with prescribed group action, Computational Aspects of Algebraic Curves, and Cryptography, Gainesville, 2003. 
  • Hyperel liptic curves with non-hyperelliptic involutions 983-14-115 AMS, Joint Mathematics Meeting, Baltimore, January 2003. 
2002
  • Hyperel liptic curves with extra automorphisms, Galois Theory Conference, John Thompson’s 70th birthday, Gainesville 2002. 
  • Field of definition and field of moduli of hyperel liptic curves, University of Florida Colloquium, Gainesville, Florida, September 2002. 
  • Computational aspects of algebraic geometry, Algebra seminar, UC Irvine, CA, December 2002. 
  • Genus 2 curves with (3,3)-split Jacobian and large automorphism group, ANTS V, International Symposium in Algorithmic Number Theory, Sydney, 2002. 
2001
  • Automorphisms and el liptic subfields of genus 2 fields (with H. V¨olklein), 972-14-47 AMS, Southwestern Conference, Groups and Covering Spaces in Algebraic Geometry, Irvine, CA, November 2001. 
  • The automorphism group of a Riemann surface, University of Florida Colloquium, Gainesville, Florida, September 2001. 
  • Elliptic subfields and automorphisms of genus 2 curves, University of Erlangen, Germany, June 2001. 
  • Computing the locus of genus 2 fields with degree 2 or 3 el liptic subfields, Institute for Experimental Mathematics, Essen, Germany, May 2001. 
  • Some Computational Aspects of Genus 2 Curves, Number Theory Conference, University of Illinois, Urbana-Champaign, IL, May 2001. 
2000
  • Genus 2 curves covering el liptic curves, Workshop on Arithmetic Geometry, MSRI, Berkeley, CA, December 2000.
  • Modular curves and Hurwitz spaces, Conference on Topological Groups, TU-Munchen, Germany,June 2000. 
  • Curves of genus two with (n,n)-decomposable Jacobians, AG Gruppentheorie, Erlangen, Germany, March 2000. 
1999
  • Explicit equation of certain Hurwitz spaces, University of Heidelberg, Germany, May 1999. 
  • Curves of genus 2 covering el liptic curves (with V. Krishnamoorthy), 940-12-287 AMS, Southeastern Conference, Gainesville, Florida, March 1999. 
1998
  • Rigid tuples and monodromy groups, Conference on ABC-conjecture, Tucson, Arizona, March 1998. 

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