MATH 20B. (202 students. Center Hall 101, 3 p.m. TA's: pcompeau, mtiefenbruck, ashakeel, vkungurt. Grader: Schilz.) Homework 3 for Math 20B, due Friday, Oct. 16, ch. 6 review: 5, 9, 12, 21, 22, 29 (these probs. serve as review problems for midterm 1 as well); 11.3: 2, 6, 18, 20, 38; 11. 4: 4, 8, 14. On Friday, Oct. 16, Monday, Oct. 19, Monday Oct. 26 and Friday Oct. 30 we will use text and exercises from a student supplement obtainable here. HWK 4, due Friday Oct. 23 at 4 p.m. is: Supplement p. 12: 1, 2, 3, 4 ; p. 15: 1, 2, 4, 5; Book 7.1: 2, 6, 25. HWK 5 due Thurs. Oct.29: section 7.2: 2, 16, 22, 28, 49; 7.3: 2, 62; 7.4: 2,4, 54; 7.5: 2, 6; Supplement 3.2: 3, 5. HWK 6 due Thurs. Nov. 5: section 7.6: 2, 4, 12, 13, 44, 58; 7.7: 2, 4, 8, 13, 57, 60, 79; Supplement 4.4: 2 and Supplement 5.6: 1, 3, 4. MIDTERM 2 on Friday November 13 will cover chapter 7, including partial fractions, and complex numbers including polar form of these. Homework 7 due Thurs. Nov. 12 is section 10.1: 2, 14, 28, 34, 52; 10.2: 2, 4, 18, 39. Homework 8 due Thurs. Nov. 19, 10.3: 6, 10, 20, 24, 30, 36, 64; 10.4: 2, 8, 9, 14, 26. HWK 9 due Wed. Nov. 25: section 10.5: 2, 8, 10, 35, 44; 10.6: 2, 4, 32, 38; 10.7: 2, 14, 37, 48.
OFFICE HRS. AND GRADES. Off. hrs. are after the lectures outside the lecture hall for the rest of the term. Grading is both my courses is on a curve suggested on p. 10 under visitor guidebook, instructor resources of math department's website. The weighting in Math 20B (from the first day) is 20% Midterm 1, 25% Midterm 2, 15% Homework (and/or quizzes, here the detailed policy set by your TA), 40% Final. In Math 20E it is 20% each midterm, 10% Homework, and 50% Final.
MATH 20E. (198 students, Warren Lecture Hall 2005, 11 a.m. TA's: r1gomez, htn005, jmiddleton. Grader: Swartz.) Math 20E homework here You may substitute 12 for 11 in 4.2 homework. Math 20E vector calculus midterm 1 date for my 11 o'clock lecture changed to Wednesday Oct. 21 in class. Homework 4 is due Friday because of the wednesday midterm. The midterm 1 covers everything on the syllabus from chapter one up to and including chapter 4.4 (divergence and curl). MIDTERM 2 will be in class on Wednesday Nov. 18 and cover material we studied up to and including surface integrals of vector fields, section 7.6.
PUBLICATION LIST. Printable version
WHAT'S NEW. A notion of induction-restriction depth of multimatrix algebra inclusions applied to subgroups with Sebastian M. Burciu and Burkhard Kuelshammer.
RESEARCH. Mainly in the areas of Ring Theory, Quantum Algebra, and Quantum Groupoids. More specifically, noncommutative Galois theory; Hopf algebras, Hopf algebroids, weak Hopf algebras, groups and their actions; modules, subrings and induced representations; algebraic subfactor theory.
Secondary interests are in other aspects of homological algebra, cyclic homology, knot theory, commutative algebra, subfactors, K-theory, algebraic topology, representation theory, noncommutative geometry, Lie algebroids and Poisson geometry. An essay about connections with physics, analysis and geometry.
VISITS, TALKS AND CONFERENCES. L.S.U. talk, MSRI, Brussels, Budapest, V.U.B. Workshop talk, Odense colloquium, Oslo, Swansea talk, Leeds talk, Cambridge Mass., Bergen, Karlstad talk, Mainz talk, Spa Belgium, Oslo colloq., Algebra, Geometry and Math. Phys., Göteborg talk, Norwegian algebra meeting, AQuA, Noncommutative Structures in Math and Physics talk. U.S.A. algebra seminar. Jena, Summer meeting, Canadian Math Society, June 6-8, 2009 Talk. Texas A & M University, Algebra and Combinatorics Seminar
RECENT PREPRINTS. Subgroups of depth three and more with Sebastian Burciu, to appear in the Proc. Royal Flemish Acad. Skew Hopf algebras, irreducible extensions and the pi-method, to appear in Münster Journal of Mathematics, special issue dedicated to Joachim Cuntz on the occasion of his sixtieth birthday. When weak Hopf algebras are Frobenius with Mio C. Iovanov will appear in the Proceedings of the American Math Society Semisimple Hopf algebras and their depth two Hopf subalgebras is merged with S. Burciu's Depth two Hopf subalgebras of a semisimple Hopf algebras and appeared July in Journal of Algebra.
OPEN PROBLEMS. In the Oslo, Karlstad, Mainz, Leeds and Canada talks above, some background for several problems in depth two (and more): 1) Are left D2 extensions right D2? 2) Are D2 Hopf subalgebras normal? Answer is now known to be YES. 3) Do D2 extensions of simple algebras have a Galois correspondence between subextensions and Hopf subalgebroids? 4) Is a fin. gen. bialgebroid the endomorphism ring of a D2 algebra extension? (5) Are there subgroups of minimimum depth 2n where n > 3? (6) Find a characterization of depth n subgroup (e.g. n = 2 <=> normal subgroup).
Are biseparable extensions Frobenius? See article (K-Theory 24 (2001), 361-383) by Caenepeel and myself for terminology in this problem.
POSTS. Ċrhus, Denmark, Luminy, Roskilde: IMFUFA (now defunct institute), Copenhagen: Professorabel, Heidelberg University (see snapshot below), Trondheim, Norway, (see snapshot to your right), Munich, Düsseldorf, NorFA researcher at Chalmers in Göteborg, University of New Hampshire in Durham. University of Pennsylvania in Philadelphia. Lousiana State University in Baton Rouge.
UNDERGRADUATE TEACHING. Math 4201, Galois theory, in the spring of 2008 at LSU as well as Math 1441. Calculus I and Calculus III at Penn in the fall, and Math 180 in the spring of 2007. At UNH, Introduction to mathematical proof, Calculus I, Mathematical modelling for life sciences graduates, Intro. to PDE's, an evening class in Calculus I, Abstract Algebra, Diff. Eqs. with Linear Algebra, Abstract Algebra with Projective Geometry. Nine undergraduate courses in Norway/Denmark in linear algebra, projective geometry, differential equations, algebra and mathematics education.
MONOGRAPH. New Examples of Frobenius Extensions, volume 14 in the American Mathematical Society's University Lecture Series.
Note added in 2009: I am in the very early planning stage for a second volume of "New Examples..." It might include chapters on depth two and reconstruction of weak Hopf algebras on separable centralizers, Hopf algebras on one-dimensional centralizers, Hopf algebroids and Galois theory, antipodes and double algebra structures for Frobenius extensions, Frobenius algebras in categories and separability. Some of this theory is cited in Khovanov's Link Homology and Frobenius Extensions, Manin's Real Multiplication and Noncommutative Geometry, Van Oystaeyen and Panaite's Some bialgebroids constructed by Kadison and by Connes-Moscovici are isomorphic, and Brzezinski and Böhm's Strong connections and the relative Chern-Galois character for corings and some of this may find its way into the new volume. See the link to updated and annotated list of references to "New Examples..."
RECENT, FUTURE AND MAIN PUBLICATIONS. Simplicial Hochschild cochains as an Amitsur complex has appeared in J. Gen. Lie Theory in 2008 (by a fluke arXiv has the better version of this paper) . Finite depth and Jacobson-Bourbaki correspondence, appeared in the Journal of Pure and Applied Algebra in July 2008. Pseudo-Galois extensions and Hopf algebroids appeared July 4, 2008, in Birkhauser Trends in Math, Proceedings of Conf. on Modules and Comodules, Portugal, Sept. 2006, on the occasion of Robert Wisbauer's birthday (overlooked by Mathscinet for some reason). Bialgebroid Actions on Depth Two Extensions and Duality with coauthor Kornel Szlachanyi appeared in October 2003 in volume 179 of Advances in Mathematics. With coauthor Dmitri Nikshych, Frobenius extensions and weak Hopf algebras appeared in volume 244 (2001), 312-342, in Journal of Algebra, and our paper, Hopf algebra actions on strongly separable extensions of depth two appeared in no. 2, vol. 163 (2001) in Adv. in Math. The rest of my publications, or anyone's for that matter, are summarized by Zentralblatt or MR lookup which has homepage www.ams.org/mrlookup (with a lag of about one year from date of publication).
TEXTBOOK. Projective Geometry and Modern Algebra with coauthor Matthias Buch-Kromann
EDUCATION. Bachelor's degree from Princeton University, Ph.D. from UC Berkeley in 1989 with a dissertation on cyclic homology.
INTERESTING QUOTES. "The practical purpose of a mathematical research article is to increase understanding among the researcher's mathematical colleagues, not just to increase their admiration for the author," Lie and Klein, 1871.
REFEREE. Refereeing of papers submitted to journals is anonymous in mathematics. It might be helpful to discuss openly what should be general guidelines for do's and don'ts as a referee. My work as a referee (of papers on Frobenius extensions and related theory) is characterized by returning a review in about four months or less with a high approval rate. I was forced to rate two papers several years ago critically for substandard presentation and content. In principal I would like to replace that referee who took one or more years to write a review of little scientific content.
MATHEMATICAL ANCESTORS. According to the math geneology project, my Ph.D. supervisor and his supervisor are in reverse iteration: John Wagoner, Princeton, 1966; William Browder, Princeton, 1958; John C. Moore, Brown, 1952; George Whitehead, Jr., Chicago, 1941; Norman Steenrod, Princeton, 1936; Solomon Lefschetz, Clark, 1911; William Story, Leipzig, 1875; Wilhelm Scheibner, Halle, 1848; Karl Jacobi, Berlin, 1825.