Mailing address:
113 W 60th St Room 813
New York, NY 10023
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Courses Taught at Fordham University:
Finite
Mathematics, Calculus I, Calculus II, Probability, Statistics,
Linear Algebra, Numerical Analysis, Mathematics of Finance.
Biography:
David Swinarski majored in math and English at the
University of Notre Dame, graduating in 2001. As an undergraduate
he also did research in computational
organic chemistry with Olaf Wiest. Swinarski received a Marshall
Scholarship in 2000 to study at the University of Oxford in
England. He completed his master's degree in 2003 under the
direction of Frances Kirwan. He received his Ph.D from Columbia University in
2008 under the direction of Michael Thaddeus
and Ian Morrison (Fordham University). He held a postdoctoral
research position at the University of Georgia in Athens (UGA) from
20082011, where he worked with Valery Alexeev and Angela Gibney.
Dr. Swinarski joined the Fordham faculty in August 2011.
Current
Interests and Research:
Dr. Swinarski's research interests include algebraic geometry (the study
of polynomial equations) and mathematical finance. His current research
topics include geometric invariant theory, birational geometry of
moduli spaces of curves, vector bundles of conformal blocks, and
automorphisms of curves. Dr. Swinarski actively collaborates
with researchers at Fordham, UGA, Columbia, Boston College, as well as undergraduates at Fordham University.
Publications:
Selected recent publications:
 "sl_n level 1 conformal block divisors on
$\bar{M}_{0,n}$". With Maxim Arap, Angela Gibney, and James
Stankewicz. International Mathematics Research Notices
2011.
 "Gröbner techniques for low degree Hilbert
stability." With Ian Morrison. Experimental
Mathematics, 2011.
 "GIT stability of weighted pointed curves."
Transactions of the American Mathematical Society, 2012.
Full publication list
Preprints, drafts, and slides from talks
Undergraduate research:
Six undergraduates from UGA worked with Dr. Swinarski in Fall
2010 on equations of curves with automorphisms.
Eight undergraduates from Fordham University have worked with
Dr. Swinarski from 2011 to the present on conformal blocks and
fusion rules. More
information
Computer work:
Dr. Swinarski uses several computer packages including Sage, Magma, Macaulay2, and
Excel in his research and teaching. Portfolio
of Dr. Swinarski's computer work
