Higher Education 

Matriculation at the University of Copenhagen (Mathematics and
Computer Science) in the summer of 1985.

Examination for the Master's Degree in January 1991. Master's Thesis
handed in in December 1991. Master's Degree obtained on
January 2, 1992.

Title of Master's Thesis: "Proendelige grupper og eksempler
på disses realisering som Galoisgrupper".
("Profinite groups and examples of their realisation as Galois
groups", Danish.) Thesis supervisor: Prof. C. U. Jensen,
Copenhagen.

 
Introductory stipend from the Faculty of Natural Sciences at the
University of Copenhagen from April to July 1992.

 
Received travel grant from Rejselegat for Matematikere
("Travelling scholarships for Mathematicians")
in the spring of 1992.
Grant used for visiting the University of Heidelberg, Germany,
in the period October 1992 to July 1993.

 
Obtained Ph.D.stipend at the University of Copenhagen for the period
September 1993 to August 1996.

 
Received gold medal from the University of Copenhagen for the prize
paper "Galoisteoretiske indlejringsproblemer og realisering af
pgrupper som Galoisgrupper" ("Galois theoretical
embedding problems and realisation of pgroups as Galois
groups", Danish) in November 1994.
The paper was written in the autumn of 1993.

 
Spent the period from February 2, 1995, to June 15, 1995, at the
University of TelAviv, Israel, as a visitor of Prof. M. Jarden.

 
Obtained Ph.D. degree from the University of Copenhagen in
September 1996.

Title of Ph.D. thesis: "Galois Theoretical Embedding Problems
with Cyclic Kernel of Prime Order". Thesis supervisor:
Prof. C. U. Jensen, Copenhagen. Evaluation commitee:
Prof. Dr. A. Prestel (Konstanz, Germany), Prof. J. B. Olsson
(Copenhagen) and Dr. G. Brattström (Stockholm, Sweden).


Postdoctoral Employment 

July 1997June 1999: ARC Postdoctoral Fellow at the Department
of Mathematics at Queen's University, Kingston, Ontario.
Supervisors: Prof. R. Murty and Prof. N. Yui.

 
August 1999December 1999: Visitor at the Mathematical Sciences
Research Institute in Berkeley, California, attending the research
program "Galois Groups and Fundamental Groups".

 
January 2000June 2000: Postdoctoral Fellow at the Department of
Mathematics at Queen's University, Kingston, Ontario, continuing work
with Prof. N. Yui. The entire period August 1999 to June 2000
financed by the Danish Natural Science Research Council.

 
August 2000December 2000: General Member at the Mathematical
Sciences Research Institute in Berkeley, California, attending the
research program "Algorithmic Number Theory".

 
January 2001May 2001: Research fellow at Tokyo Metropolitan
University, Japan, visiting Prof. Katsuya Miyake.

 
July 2001June 2002: Postdoctoral fellow at the University
of Waterloo, Ontario. Supervisor: Prof. C. Stewart.

 
September 2002August 2008: Assistant professor at Texas Tech University.

 
September 2008: Associate professor at Texas Tech University.


Teaching Experience


During Ph.D. work: Teaching assistant on the course Math 1MA
(introductory calculus, first year) in the spring semester of 1994;
instructor on the course Math 3AL (elementary group and Galois theory,
third year) in the autumn semester of 1994; instructor on the the
course Math 3AG (introductory algebraic geometry, third year) in
the spring semester of 1996; organizer (together with J. B. Olsson)
of the algebra seminar (various algebraic topics, graduate level)
in the spring semester of 1996; and lecturer (together with
C. U. Jensen) on the course Math 4AL (topics in Galois theory,
graduate level) in the spring semester of 1996.

 
After completion of Ph.D. work: Teaching assistant on the course
Math X (elementary number theory and combinatorics, first year) in
the autumn semester of 1996; and teaching assistant for the first
year repetition class.

 
All of these classes/courses were taught at the Department of
Mathematics, University of Copenhagen.

 
As Postdoctoral fellow at Queens's: Math 128
(introductory calculus for engineering students) in the fall
semester of 1997; Math 111 (linear algebra) in the fall semester
of 1998 and the winter semester of 1999; and APSC 174 (linear algebra)
in the winter semester of 2000. Also in the winter semester of 2000,
a graduate course (Math 912) entitled "Constructive aspects of
inverse Galois theory" with Prof. N. Yui.

 
At Tokyo Metropolitan University: Two sets of seminar talks
for graduate students: "Generic polynomials and the Noether
Problem" and "Generic extensions" on February
2223, 2001, and "Generic polynomials, pgroups in
characteristic p" and "Essential dimension,
cyclic groups" on April 2425, 2001.
(The latter being four onehour talks given during two twohour
sessions.)

 
At the University of Waterloo: Math 115 (Linear algebra for
engineering students) in the fall term of 2001. Math 118
(Calculus for engineering students) and PMath 340 (Elementary number
theory) in the winter term of 2002.

 
At Texas Tech University: See the
teaching page.


Selected Talks


Embedding Problems with Cyclic Kernel of Order 4.
UF Galois Theory Week, University of Florida, Gainesville.
October 17, 1996.

 
Nonsplit Embedding Problems with Kernel of Order 2.
Department of Mathematics Colloquium, Purdue University.
December 9, 1997.

 
Embedding Problems and Equivalence of Quadratic Forms.
Mathematics Department Algebra Seminar, University of Western Ontario.
February 17, 1998.

 
Parametrization of Galois extensions.
Karcher Colloquium, University of Oklahoma.
September 3, 1998.

 
Realization and parametrization of certain 2group extensions.
Algebra Topics Seminar, University of Oklahoma.
September 4, 1998.

 
Parametric Descriptions of Galois Extensions.
Department of Mathematics Colloquium, Purdue University.
November 17, 1998.

 
Some small 2Groups as Galois Groups.
CMS Winter Meeting, Kingston.
December 14, 1998.

 
Generic and Explicit Realisation of small pGroups.
Konstruktive Methoden in der Galoistheorie, Dagstuhl, Germany.
July 20, 1999.

 
Brauer Type Embedding Problems.
Galois Topics Research Seminar, MSRI.
September 30, 1999.

 
Dihedral groups over Q.
Galois groups and modular forms, Saga University, Japan.
December 14, 1999.

 
Brauer type embedding problems.
Conference on Algebra and Algebraic Geometry with Applications
(Celebration of the seventieth birthday of Professor S. S. Abhyankar),
Purdue University.
July 26, 2000.

 
Essential Dimension.
Algorithmic Number Theory Seminar, MSRI.
October 2, 2000.

 
Generic polynomials for Galois extensions.
Algebra Seminar, University of Alberta.
December 8, 2000.

 
Generic descriptions in Galois theory.
Number Theory Seminar, Tokyo Metropolitan University.
February 6, 2001.

 
Constructing generic polynomials.
Number Theory Workshop, Waseda University, Tokyo.
March 12, 2001.

 
Generic polynomials.
Seminar, Reed College, Oregon.
September 27, 2001.

 
Essential Dimension.
Algebra Seminar, University of Western Ontario.
December 6, 2001.

 
pGroups in characteristic p.
Pingree Park "Brauer Group" Meeting, Colorado State
University.
July 6, 2002.

 
D_{p}Extensions in characteristic p.
Galois Theory Conference in Honour of John Thompson's 70th Anniversary,
University of Florida, Gainesville.
November 7, 2002.

 
Generic polynomials.
Algebra Seminar, University of Texas at Austin.
September 23, 2003.

 
Generic polynomials.
Algebra and Geometry Seminar, University of Valenciennes, France. June 23, 2004.

 
Generic polynomials.
GTEM Seminar, University of Lille, France. June 25, 2004.

 
Generic polynomials with one parameter.
Pingree Park "Brauer Group" Meeting, Colorado State
University. July 2, 2004.

 
PSL(2,2^{n}) as Galois group over GF(2^{n}).
C. U. Jensen Symposium, University of Copenhagen. September 3, 2004.

 
Groups with essential dimension 1.
Workshop on the Inverse Galois Problem and Galois Covers,
Kochi University, Japan. November 2, 2004.

 
The Monge shuffle for a deck with 2^{n} cards.
MAA General Contributed Papers Session, Joint Mathematics Meetings,
Atlanta. January 8, 2005.

 
Essential dimension.
Number Theory Workshop, Waseda University, Tokyo.
March 18, 2005.

 
Essential dimension.
Session on Classical and Differential Galois Theory,
AMS Sectional Meeting, Texas Tech University. April 9, 2005.

 
Generic polynomials.
AMS Special Session on Division Algebras, Galois Theory, Cohomology and
Geometry, Joint Mathematics Meetings, San Antonio. January 13, 2006.

 
Quaternion groups as Galois groups.
Special Session on Representation Theory and Galois Cohomology in Number Theory,
AMS Sectional Meeting, Davidson College. March 4, 2007.

 
PGL_{3} as a differential Galois group.
Special Session on Differential Algebra,
AMS Sectional Meeting, Stevens Institute of Technology. April 15, 2007.

 
Differential Galois extensions with Galois group PGL_{2}.
Pingree Park "Brauer Group" Meeting, Colorado State University. July 4, 2008.

 
PGL_{n} as a differential Galois group.
Third International Workshop on Differential Algebra and Related Topics
(DART III), Rutgers University, Newark. November 14, 2008.

 
Spin_{7} as a differential Galois group.
Special Session on Brauer Groups, Quadratic Forms, Algebraic Groups, and Lie Algebras,
AMS Sectional Meeting, North Carolina State University. April 4, 2009.

 
Generic polynomials for cyclic groups.
Kibbutz Ketura "Brauer Group" Meeting, Israel. January 10, 2010.

 
Spin groups as differential Galois groups.
AMS Special Session on Differential Galois Theory and Group Representations:
A Tribute to Andy Magid, Joint Mathematics Meetings, San Francisco. January 15, 2010.

 
Generic polynomials and essential dimension of finite groups.
Essential dimension and Cremona groups, Chern Institute of Mathematics, Tianjin, China. June 15, 2012.

 
Nonconnected groups as differential Galois groups.
Pingree Park "Brauer Group" Meeting, Colorado State University. August 10, 2012.

 
Quaternion groups as Galois groups.
Galois groups and Brauer groups (in honour of Jack Sonn), Technion, Haifa, Israel. January 7, 2013.

 
Finite groups as differential Galois groups.
Pingree Park "Brauer Group" Meeting, Colorado State University. June 12, 2015.


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