|
Prof. PETER MAGYAR
|
|
Address:
|
Department of Mathematics
Michigan State University
East Lansing, MI 48824-1027
| Email:
|
magyar at math dot msu dot edu
|
|
Office:
| Wells Hall D-326
|
Phone:
| 517-353-6330
|
Fax:
| 517-432-1562
| | | |
I am Associate Professor at
the Michigan State Math Department.
In Spring 2014 I teach
Math 482 (Discrete Math II).
Some previous courses:
Math 132 (Calculus I),
Math 299 (Transition to Formal Mathematics),
Math 309 (Advanced Linear Algebra),
Math 310 (Abstract Algebra),
Math 418H−419H (Honors Abstract Algebra),
Math 481 (Discrete Math I),
Math 482 (Discrete Math II),
Math 880 (Graduate Combinatorics I);
also, my daily-quiz system for upper undergrad courses.
In elementary terms, group theory is the theory of symmetry. A symmetry is any way of moving an object onto itself, and the set of all symmetries of an object is its symmetry group. This has a natural binary operation: perform one symmetry after another to get a new symmetry; and this makes the symmetry group into something resembling a number system.
A Lie group is the continuous symmetry group of a highly symmetric object such as the circle or the sphere.
Representation theory starts with an abstract group (considered purely as an algebraic system) and describes the objects which have this symmetry.
My main field is representation theory, using tools from algebraic combinatorics and algebraic geometry. I study semi-simple complex Lie groups and the associated loop groups, representations, and homogeneous spaces (Grassmannians, flag varieties, affine Grassmannians). I am interested in Young tableaux and their generalizations, such as Littelmann paths and Kashiwara crystals. I have also done work on Schubert calculus and (affine) Schubert polynomials.
See my research statement and
abstract.
- On ideal generators for affine Schubert varieties,
with
V. Kreiman,
V. Lakshmibai,
and
J. Weyman, in Algebraic groups and homogeneous spaces, 353--388, Tata Inst. Fund. Res. Stud. Math., Tata Inst. Fund. Res., Mumbai, 2007.
-
Littelmann paths for the basic representation of an affine Lie algebra,
Journal of Algebra 305 (2006), 1037--1054.
Preprint
- Standard bases for affine SL(n)-modules,
with V. Kreiman, V. Lakshmibai, and J. Weyman,
International Mathematics Research Notices 2005, No. 21.
-
Bruhat order for two flags and a line, P. Magyar,
Journal of Algebraic Combinatorics 21 (2005).
-
Standard monomial theory for Bott-Samelson
varieties,
V. Lakshmibai,
P. Littelmann and P. Magyar,
Compositio Mathematica 130 (2002), 293-318.
-
Symplectic multiple flag varieties of finite type,
P. Magyar, J. Weyman and
A. Zelevinsky,
Journal of Algebra 230
(Buchsbaum Festschrift, 2000), 245-265.
-
Multiple flag varieties of finite type,
P. Magyar,
J. Weyman and
A. Zelevinsky,
Advances in Mathematics
141 (1999), 97-118.
-
The Space of triangles, vanishing theorems,
and combinatorics,
W. van der Kallen and P. Magyar,
Journal of Algebra
222 (1999), 17-50.
-
Standard monomial theory and applications,
V. Lakshmibai,
P. Littelmann and P. Magyar, in
Representation Theories
and Algebraic Geometry, A. Broer (ed.), Kluwer
Academic Publishers, Boston (1998).
-
Degeneracy Schemes and Schubert varieties,
V. Lakshmibai and P. Magyar,
International Mathematics Research Notices
12 (1998), 627-640.
-
Standard monomial theory for Bott-Samelson
varieties of GL(n),
V. Lakshmibai and P. Magyar,
Publications of RIMS Kyoto 34 (1998), 229-248.
-
Standard monomial theory for Bott-Samelson
varieties,
V. Lakshmibai and P. Magyar,
Comptes Rendues Acad. Sci. Paris, Ser I 324 (1997), 1211-1215.
-
Schubert polynomials and Bott-Samelson varieties,
P. Magyar,
Commentarii Mathematici Helvetici
73 (1998), 603-636.
-
Borel-Weil theorem for configuration varieties
and Schur modules, P. Magyar,
Advances in Mathematics 38 (1998), 328-366.
-
Random walk in a Weyl chamber and
the decomposition of tensor powers,
D. Grabiner and P. Magyar, Algebraic Combinatorics
2 (1993), 239-260.
-
Formulas for Generalized Kazhdan-Lusztig
Polynomials,
doctoral thesis, 50pp, Harvard University, 1993.
My papers on the
Math ArXiv.
Manuscripts and Notes
Collaborators & Friends
Education
Employment
-
University of Utrecht, Netherlands,
Postdoctoral Research Fellow, 1993-95
-
Université de Paris VII,
Visiting Scholar, April-May 1995
-
Northeastern University,
Visiting Assistant Professor, 1995-98
-
Brandeis University,
Visiting Assistant Professor, 1998-2000
-
Michigan State University
Assistant Professor, 2000-2006
Associate Professor, 2006-present
Honors
Personal
I was born in Budapest,
Hungary, and immigrated
with my family at age 4. I speak Hungarian and
have visited the country many times, including Junior year
abroad in the
Budapest Semesters in Mathematics program (1985).
Family.
Information
Math Resources Online Florida State Guide
Electronic Journals
American Journal of Mathematics
American Mathematical Monthly
Annals of Mathematics
AMS Journal, Proceedings, Transactions
Royal Society of London Proceedings, Philosophical Transactions
NUMDAM French Journal Archive
Compositio Mathematica
Publications mathematiques de l'IHES
Annales scientifiques de l'ENS,
Fourier, Grenoble, Blaise Pascal, Henri Poincaré
Séminaires Bourbaki, Cartan, Chevalley, Dubreil, Ehresmann, Grothendieck, Leray, Sophus Lie, Samuel, Schützenberger
EMANI Journal Archive
Inventiones Mathematicae
Communications in Mathematical Physics
Journal of Algebraic Combininatorics
Michigan Mathematical Journal
Experimental Mathematics
Commentarii Mathematici Helvetici
Mathematische Annalen
Mathematische Zeitschrift
Pictures: Real projective plane,
Whitney umbrella, triangular lattice graph paper.
Regular polytopes. 3D:
dodecahedron
icosahedron.
4D:
5-cell,
8-cell,
16-cell,
24-cell,
120-cell,
600-cell.
Kinawa-Chippewa Math Circle.
Handouts:
Modular Arithmetic,
Public-Key Cryptography.
