CV
Publications
Talks&Lectures
CURRICULUM VITAE
Date of birth:
Education
B.S and M.S in Mathematics: 1987, Al.I.Cuza University of Iasi, Romania .
PhD in
Mathematics: 1994, Michigan
State University,
Thesis advisor: Professor Thomas H. Parker.
Awards
·
``Gheorghe Tzitzeica'' Prize of the
· NSF Grant DMS-0071820, 2000-2003.
· NSF Grant DMS-0303601, 2003-2006
Work experience
Associate Professor ,
Visiting scholar, Fourier
Institute,
Visiting scholar, The
Assistant Professor,
Postdoctoral Fellow, Mc Master University, Ontario, Canada, 1997-1998
Assistant Professor,
Visiting scholar,
Teaching Assistant, Michigan State University, 1990-1994.
Research interests
My field of expertise is global analysis with an emphasis on the geometric applications of elliptic partial differential equations arising from gauge theory, symplectic geometry and index theory for Dirac operators.
Almost complete list of publications
SOME THINGS THAT I WROTE
57.
On the total
curvature of semialgebraic graphs arXiv:
0806.3683 We define the total curvature
of a compact connected one dimensional
semialgebraic subset $\Gamma$ of
$\mathbb{R}^3$ as an integral $K(\Gamma)=\int_\Gamma d\mu$, where $\mu$ is a
certain Borel measure completely
determined by the local extrinsic geometry of $\Gamma$. We prove that it satisfies the Chern-Lashof inequality $K(\Gamma)\geq b(\Gamma)$, where
$b(\Gamma)=b_0(\Gamma)+b_1(\Gamma)$, and we
completely characterize those
graphs for which we have equality. We
also prove the following unknottedness result:
if $\Gamma\subset \bR^3$ is homeomorphic to the suspension of an
$n$-point set, and satisfies the
inequality $K(\Gamma)
<2+b(\Gamma)$, then $\Gamma$ is unknotted. Moreover, we
describe a simple planar
graph $G$ such that for any $\varepsilon>0$ there
exists a knotted semialgebraic
embedding $\Gamma$ of $G$ in $\bR^3$
satisfying $K(\Gamma)<\varepsilon
+b(\Gamma)$.
56. On a
Bruhat-like poset arXiv:
0711.0735 We
investigate the poset of strata of the stratification introduced in the
paper 55.
55. Schubert calculus on the Grassmannian of
hermitian lagrangian subspaces arXiv:
0708.2669 We describe a Schubert like stratification on the Grassmannian of hermitian lagrangian spaces in
$\mathbb{C}^n\oplus \mathbb{C}^n$ which is natural compactification of the space of
hermitian $n\times n$ matrices.
The closures of the strata define integral
cycles, and we investigate their
intersection theoretic properties.
The methods employed are Morse
theoretic.
54. Tame flows
math.GT/0702424,
The tame flows are nice flows on nice spaces. The nice
sets are the pfaffian sets introduced by Khovanski, and a
flow on such a set is tame if the
flow map is pfaffian. Any compact tame set
admits plenty tame flows. We
prove that the flow determined by the gradient of generic
real analytic functions with
respect to a generic real analytic
metric is tame. The typical tame
gradient flow satisfies the Morse-Smale condition , which
in the tame context is equivalent to the
fact that the stratification by unstable
manifolds is Whitney regular. We explain how to compute the the Conley indices of isolated
stationary points of tame flows in terms of their unstable varieties,
and then use this technology to produce a Morse theory on posets
generalizing R. Forman’s discrete Morse theory. Finally, we
use the Harvey-Lawson technique to
produce a homotopy between the DeRham
complex of a smooth manifold and the
simplicial chain complex associated to a triangulation.
53. Curvature
measures I like very
much how these notes turned out. This is an old subject, and in these notes I dress it in some new
clothes.
52. Metoda functiilor generatoare (``Gazeta Matematica’’,
2007’). Try this if you can read Romanian.
51. Morse functions statistics, math.GT/0604437, Functional Analysis and Other Applications,
1(2006), 97-103. I answer a question of V.I.
Arnold concerning the growth of the number of Morse function on the 2-sphere. Read
more about this problem.
50. Counting Morse functions on the 2-sphere,
math.GT/0512496.
This paper
is inspired by earlier work of V.I. Arnold. We compute the
number of excellent Morse functions on
the two sphere. To appear Compositio Mathematica
49. The anatomy of a singularity, These are notes for a Felix Klein Seminar.
48. Notes on Morse theory,
These are notes for
the Fall 2005, “Topics
in topology” course.
47. On a multidimensional checkers game, This is a generalization of
a problem from the
46. The
Euler characteristic, Some nice
consequences of really elementary tricks.
45. Characteristic currents of singular connections
43. Notes on
the Atiyah-Singer index theorem, These are notes for the Math 658 , Spring 2004 course, “Topics in topology”.
42. Microlocal studies of shapes I
begin by describing two classical instances where the conormal cycle makes its
appearance and then I describe its construction
in the special case of simplicial complexes.
41. Derangements and asymptotics of Laplace transforms of polynomials math.CO/0401281 & New York Journal of Mathematics, v.10(2004), 117-131. This is an amusing elementary problem with surprising ramifications.
40. “Motivic”
Integral Geometry Here I am
trying to understand a beautiful little paper of Pierre Schapira. For an approach to this problem using
tame geometry check here.
39. The
Poincare-Verdier duality
38. Chern classes of singular algebraic varieties, Try this link from time to time.
37. On the curvature of singular complex hypersurfaces,
Talk at the Felix
Klein Geometry Seminar, Fall 2003, Notre Dame.
36. The many faces of the
Gauss-Bonnet theorem, This
little expository paper is an extended version of my talk at the Graduate Student Seminar,
Fall 2003.
35. Three-dimensional Seiberg-Witten
theory, Notes for a
mini-course in
34. Notes on the topology of
complex singularities , (PDF, Revised
32. Homeomorphisms vs. Diffeomorphisms (PDF, 8
pages) This little expository paper is an extended
version of my talk at the 2003 ``First year
graduate students
31. Residues and Hodge Theory (PDF,
23 pages) This expository paper is an
extended version of my talks at Karen Chandler's ``Absolutely
fabulous algebraic geometry seminar''.
30. Solutions to some
problems in Hatcher's Algebraic Topology book.
29. Seiberg-Witten invariants and surface singularities III. Splicings and cyclic covers, math.AG/02071018 (joint with Andras Nemethi) We prove the conjecture formulated in 25 for suspension sigularities, i.e. isolated surface singularities of the form z^n+ f(x,y)=0, where, f(x,y)=0 is an irreducible plane curve.
28. Seiberg-Witten invariants and surface singularities. (PDF, 8 pages) This is a summary of 25 and 26.
27.Of shapes, differentials and integrals. (PDF, 8 pages) This little expository paper is an extended version of my talk at the 2002 ``First year graduate student seminar''.
26. Seiberg-Witten invariants and surface singularities II. Singularities with good $C^*$-action, math.AG/0201120 (joint with Andras Nemethi) We prove that the geometric genus of an isolated quasihomogeneous surface singularity whose link is a rational homology sphere is completely detremined by the Seiberg-Witten invariant and the Gompf invariant of the canonical spin^c structure on the link of this singularity. When the sigularity is smoothable this implies that the Seiberg-Witten invariant of the canonical spin^c structure is -1/8 the signature of the Milnor fiber. Note although these singularities are analytically rigid some are neither Gorenstein, nor rational. Which is then the best rigidity condition?
25. Seiberg-Witten invariants and surface singularities I, math.AG/0111298, Geometry and Topology, 6(2002), 269-328, (joint with Andras Nemethi) We formulate a conjecture relating analytic invariants of isolated surface singularities to topological invariants of the links of those singularities, which are assumed to be rational homology 3-spheres. More precisely we show that the link of such a singularity is equipped with a canonical spin^c structure. We conjectured that if the singularity is Gorenstein or rational then its geometric genus is determined in a simple explicit fashion by the Seiberg-Witten invariant and the Gompf invariant of this canonical spin^c structure. To support this conjecture we establish its validity on many classes of singularities: Brieskorn, cyclic quotient singularities, A-D-E singularities, polygonal singularities etc. This considerably generalizes earlier results of Fintushel-Stern, Neuwmann-Wahl.
24. Seiberg-Witten invariants of
3-manifolds. Part 1 (PDF, 98 pages) This unfinished manuscript describes in great detail
the construction of SW theory of 3-manifolds, closed or with boundary. It has
considerable overlap with published work of Yuhan Lim and Marcolli-Wang (which
is why I never finished it and I will never publish it). However, I adopt a
sufficiently new point of view to make it useful for references. In particular,
I am careful in figuring out the various signs. There are a couple of other
folklore results for which I could not find references.
23. Seiberg-Witten invariants of rational homology
spheres (PDF, 31pages), math.GT/0103020,
Comm. Contem. Math. I prove that for rational homology 3-spheres SW
invariant <==> Casson-Walker invariant + Reidemeister torsion.
22. Geometric connections and geometric Dirac operators on contact manifolds, (PDF, 37 pages), math.DG/0101155, Diff. Geom and its Appl.. We construct several natural connections and Dirac type operators on a general metric contact manifold which are more sensitive to the geometric background. In the special case of CR manifolds these connections are also compatible with the CR structure and include among them the Webster connection. We also describe several Weitzenbock type formulae. Our method is based on work of P. Gauduchon applied to two almost complex manifolds naturally associated to a given metric contact manifold.
21. On the Reidemeister torsion of
rational homology spheres, (PDF) math.GT/0006181,
Int. J. of Math and Math Sci. 25(2001), 11-17. I prove that the mod Z reduction of the torsion of a
rational homology 3-sphere is completely determined by three data: a certain
canonical spin^c structure, the linking form and a Q/Z-valued
constant c. This constant is a new topological invariant of the
rational homology sphere. Experimentations with lens spaces suggest this
constant may be as powerful an invariant as the torsion itself.
20. Notes on Seiberg-Witten theory, (Monograph, xii+ 482pp, Graduate Series in Math., vol. 28, Amer. Math. Soc., 2000) What can I say about my baby!?! It has to be beautiful. It took me two years to write this book, and finally here it is. There's a lot of interesting stuff in it, such as a new and almost complete presentation of the gluing theory which you won't find elsewhere. Click on the title to learn some more about it.
19. The Reidemeister Torsion of 3-Manifolds, Walter de Guyter, January 2003. I survey, mainly through very concrete examples, various interpretations of this topological invariant. I think you will find many nice old things and new ones.
18. On
the space of Fredholm selfadjoint operators, (PDF), An. Sti.
Univ. Iasi, 53
(2007), p.209-227. This is a paper is
dedicated to the memory of my good
friend Gheorghe
Ionesei, the ultimate math poet.
You can find here his cute proof of
the Abel-Jacobi theorem.
In this paper I compare various natural topologies on the space of (possibly unbounded) Fredholm selfadjoint operators and describe which one is relevant for K-theory. In the process, I fix an error in 7 indicated to me by Bernhelm Booss-Bavnbeck and K. Furutani.
17. . Eta invariants, spectral flows and finite energy Seiberg-Witten monopoles, ( PDF file, 21 pages), "Geometric Aspects of Partial Differential Equations" -Proceedings of a Minisymposium on Spectral Invariants, Heat Equation Approach Held September 1998 in Roskilde Denmark with support from Danish Research Council; B. Boss- Bavnbek, K. Wojciechowski Editors. Contemporary Mathematics, vol.242, Amer. Math. Soc, Providence R.I., 1999.This survey summarizes the results in 10, 11 and 13. Read this first if you are interested in those papers.
16. Seiberg-Witten invariants of lens spaces. math.DG/9901071, Canad. J. Math., 53(2001), 780-808. It contains an algorithm based on the ideas in 13, for computing Seiberg-Witten invariants of lens spaces. We apply this algorithm to two problems: (i) to compute the Froyshov invariants of many families of lens spaces; (ii) to show that the knowledge of the Seiberg-Witen invariants of a lens space is topologically equivalent to the knowledge of its Casson-Walker invariant + the Milnor-Turaev torsion. Problem (i) has interesting applications concerning the negative definite manifolds bounding a given lens space. (The published version contains less information that the version on the network.)
15. On the Cappell-Lee-Miller gluing theorem, math.DG/9803154, 26 pages, Pacific J.of Math, 206(2002), 159-185. I formulate a more conceptual interpretation of the Cappell-Lee-Miller theorem using the new laguage of asymptotic maps and asymptotic exactness. Additionally, I present an asymptotic description of the Mayer-Vietoris sequence naturally associated to the Cech cohomology of the sheaf of local solutions of a Dirac type operator. I discuss applications to eigenvalue estimates and approximation of obstruction bundles arising in gauge theory.
14. Lattice points inside rational simplices and the Casson invariant of Brieskorn spheres, math.DG/9801030, Geometriae Dedicata, 88(2001), 37-53. I prove a special case of a conjecture of Kronheimer and Mrowka relating the Euler characteristic of the Seiberg-Witten-Floer homology of some Brieskorn spheres to their Casson invariant. The proof is arithmetic in nature and is based on a formula expressing certain lattice-point-counts via Dedekind-Rademacher sums.
13. Finite energy Seiberg-Witten moduli spaces on 4-manifolds bounding Seifert fibrations, dg-ga/9711006, Comm. Anal and Geom., 8(2000), 1027-1096. I extend the results of 11 to the case of Seifert manifolds. The main moment in the proof is the computation of the eta invariants of the Dirac operators arising in the solutions of the Seiberg-Witten equations on Seifert manifolds. We express these invariants in terms of the so called Dedekind-Rademacher sums. This paper extends previous work of Mrowka-Ozsvath-Yu where they studied the same problem when the 4-manifold is a cylinder. As an application of these computation we obtain (often optimal) upper bounds for the Froyshov invariant of Brieskorn homology spheres. These lead to interesting information about the intersection forms of negative definite 4-manifolds bounding such homology spheres.
12. On a theorem of Henri Cartan concerning the equivariant cohomology , math.DG/0005068, An. Sti. Univ. Iasi, 45(1999), 1-17. I give a new proof of a theorem of H. Cartan concerning the equivariant cohomology of the infinitesimally free smooth actions of compact Lie groups. The approach is based on a BRST isomorphism of J. Kalkman and the unusual strategy of connecting two genuine geometric objects (connections in a principal bundle) via a path of virtual (formal) ones. The resulting isomorphuism is described at the chain level. My interest in equivariant cohomology is due to its presence in gluing formulae for gauge theoretic invariants.
11. Eta invariants of Dirac operators on circle bundles over Riemann surfaces and virtual dimensions of finite energy Seiberg-Witten moduli spaces, math.DG/9805046, Israel J. Math., 114(1999), 61-123. This is a continuation of the paper 10. I am primarily interested in the virtual dimensions of finite energy Seiberg-Witten moduli spaces on 4-manifolds bounding a disjoint union of circle bundles over Riemann surfaces. In the special case when the manifold is a cylinder based on such a circle bundle this dimension was determined by Mrowka-Ozsvath-Yu by algebraic-geometric techniques. I use a differential-geometric approach based on the Atiyah-Patodi-Singer theorem. This requires firstly the determination of the eta invariants of some Dirac operators. I present two entirely distinct methods to achieve this. The first method relies on the Bismut-Cheeger-Dai adiabatic results while the second method is more elementary and allows me to determine the entire eta function. An important part of the virtual dimension formula is a certain spectral flow. This is determined at the end of a very delicate perturbation analysis.
10. Adiabatic limits of the Seiberg-Witten equations on Seifert manifolds, Comm. Anal. and Geom., 6(1998), 331-392. I describe explicitly the behavior of the solutions of the Seiberg-Witten equations on a Seifert 3-manifold as its natural Thurston geometry degenerates along the fibers. The adiabatic limits are abelian vortices on the base of the Seifert fibration and can be equivalently described as a zeroth order perturbation of the Seiberg-Witten equations. This perturbed equation was independently studied by Mrowka-Ozsvath-Yu.
9. Lectures
On The Geometry Of Manifolds, monograph, 475 +
pages, World
Scientific Publishing Co., 1996,
2nd Edition 2007. This is an expanded
version of the graduate course on Differential Geometry and Global Analysis I gave
at the University of Michigan in the Winter of 1996. It is addressed primarily
to the graduate students specializing in global
analysis and gauge theory.
8. On the cobordism invariance of the index of Dirac operators, Proceedings A.M.S., 125(1997), 2797-2801. I show that any cobordism between two Dirac operators $D_0$, $D_1$ defines a natural tunneling isomorphism $\ker D_0 \oplus \ker D_1^* \rightarrow \ker D_1 \oplus \ker D_0^*$. In particular, this provides a very intuitive explanation for the equality $ ind D_0= ind D_1$. This tunneling map has potential applications in the recent $spin^c$ quantization theory of V. Guillemin and his school.
7. Generalized symplectic geometries and the index of families of elliptic problems, Memoirs A.M.S., vol. 128, Number 609, 1997. This is a far reaching generalization of the first half of my thesis. I prove a ``surgery'' formula for the index of an arbitrary family of Dirac operators. This arbitrariness encompasses two aspects. The family is parameterized by an arbitrary compact CW-complex and moreover we also discuss higher K-theoretic indices. I proposed a method which deals simultaneously with both difficulties. I first cast the problem in a symplectic framework and then I deal with it using a generalization of the symplectic reduction technique. Again a central player is a higher dimensional version of the Maslov index which is given a dual interpretation, K-theoretic and symplectic. A nice byproduct of this work is an ``adiabatic proof'' of a very general result concerning the cobordism invariance of the index of families.
6. Morse theory on grassmannians, An. Sti. Univ. Iasi, 40 (1994), p.25-46. The adiabatic study in 5 relies on a finite dimensional dynamical system on a lagrangian grassmannian. In this paper we show that this flow has some very nice properties: it is the gradient flow of a natural, homologically perfect, self-indexing Morse function. This is related to work of R. Bott in the 50s. Moreover, the flow is explicitly integrable.
5. The spectral flow, the Maslov index and decompositions of manifolds, Duke Univ.J , 80(1995), p.485-534. This is essentially my PhD dissertation. I prove a gluing formula for the spectral flow of a path of selfadjoint Dirac operators (on a manifold cut in two parts by a hypersurface) in terms of an infinite dimensional Maslov index. To get a better understanding of this infinite-dimensional contribution I ``stretch'' indefinitely the neck of the separating hypersurface and then explicitly describe the behavior of this Maslov index in the adiabatic limit.
4. Rigidity of generalized laplacians and some geometric applications, Aequationes Mathematicae, 48(1994), p.143-162. One consequence of this work is that a Riemann metric is determined (up to a homothety) by its associated sheaf of (locally defined) harmonic functions.
3. A weighted semilinear elliptic equation involving critical Sobolev exponents, Differential and Integral Equations, 4(1991), p.653-671. I study the critical situations for the equations considered in the previous paper. This work extends previous results of H. Brezis and L. Nirenberg.
2. Existence and regularity for a singular semilinear Sturm-Liouville problem, Differential and Integral Equations, 3(1990), p.305-322. I study the radially symmetric solutions of a semilinear elliptic problem on a ball equipped with a radially symmetric but possibly singular metric. The singular metric defines a new critical Sobolev exponent (with respect to suitable weighted Sobolev spaces). This paper is concerned with with existence and regularity in the (singular) sub-critical case.
1. Optimal control for a nonlinear diffusion equation, Richerche di matematice, vol. 37 (1988), p.3-27. This is essentially my M.S. thesis. I solve a problem posed by J. I. Diaz and A. Friedman concerning a reaction-diffusion process at equilibrium controlled by a catalyst. The goal is to determine the optimal distribution of catalyst which produces the maximum amount of output. One also has to take into account some cost considerations. After deriving first-order optimality conditions in the form of nonlinear variational inequalities I then solve them explicitly using the technique of symmetric rearrangements.
P.S. My arXiv papers can be downloaded from HERE.
SOME THINGS
THAT MY STUDENTS WROTE
3. Two proofs of the DeRham theorem, This
is the senior thesis of my student Andrew Fanoe. He goes through two different proofs of the
classical DeRham theorem, the geometric one by H. Whitney, and the more
algebraic one due to A. Weil. I think
he improved on Weil’s presentation by using the concept of (semi)simplicial sets.
2. Asymptotics of oscillatory integrals This is the
senior
thesis of my student R. Zach Lamberty. He describes
on a concrete two dimensional
example Varcheko’s technique of investigating the asymptotics of
oscillatory integrals via toric
resolutions of the phase. Check it out ! I like how it came out.
1. Geometric
Valuations Very
nice notes by the REU students Cordelia Csar, Ryan Johnson
and Ronald Lamberty
TALKS&LECTURES
o
The
topology of complex singularities, Seminar talk at Michigan State University, September 10,
2003.at
o
3-dimensional Seiberg-Witten theory, Minicourse, Fourier Institute, Grenoble France, May 15-June 15 2003.
o The topology of complex singularities, Colloquim talk at Tulane University, April 10 2003.
o Seiberg-Witten invariants of plumbed rational homology 3-spheres, Seminar talk at Tulane University, April 10, 2003.
o Links of surface singularities, Talk at the AMS Meeting, Bloomington IN, April 4-6 2003.
o Seiberg-Witten invariants and surface singularities, Talk at the conference "Dirac operators and their neighborhood", IUPUI February 21-22, 2003.
o Seiberg-Witten invariants and surface singularities, Seminar talk, University of Texas at Austin, April 9, 2002.
o Seiberg-Witten invariants and surface singularities, Inivited talk at the "Texas Geometry and Topology Conference", Lubbock Texas, April 5-7, 2002.
o
Seiberg-Witten
invariants and surface singularities, Inivited talk at the conference "Geometry and topology in dimensions 3 and 4",
o
Seiberg-Witten
invariants of rational homology 3-spheres, Seminar talk at
o
Seiberg-Witten invariants and isolated surface singularities, (audio file) Lecture at
the Symposium on Analysis and Geometry, Fields
Institute,
o
Gauge
theoretic invariants of rational homology spheres, Seminar talk at the
o Seiberg-Witten invariants of rational homology spheres, Seminar talk at the University of Wisconsin, Madison, Sept 14, 2001.
o Seiberg-Witten invariants of rational homology spheres, Seminar talk at Tulane University, New Orleans, April 3, 2001.
o
Seiberg-Witten
invariants of rational homology spheres, Talk at the miniconference "Dirac operators
and the neighborhood", IUPUI,
o Seiberg-Witten invariants of 3-manifolds, Seminar talk at Ohio State University, October 17, 2000.
o On the aritmetic complexity of smooth 4-manifolds, Seminar talk at Ohio State University, April 17, 2000.
o Seiberg-Witten theory of lens spaces, Talk at the ``Workshop on spectral geometry, topology and non-commutative geometry'', I.U.P.U.I., March 3-4, 2000.
o On the Seiberg-Witten invariants of rational homology spheres, Talk at the AMS Meeting, Charlotte, NC, Oct. 1999.
o Finite energy Seiberg-Witten moduli spaces, Talk at the AMS Meeting, Austin Texas, Oct. 1999.
o Seiberg-Witten equations on 4-manifolds with cylindrical ends, Talk at Copenhagen University, Denmark, June 1999.
o Gluing solutions of geometric partial differential equations, Talk at Roskilde University, Denmark, June 1999.
o Froyshov invariants of lens spaces , Seminar talk, Michigan State University, October 1998.
o Froyshov invariants of Brieskorn homology spheres , Talk at the ``Pacific Rim Geometry Conference'', Vancouver, British Columbia, June 1998.
o Spectral flows, eta invariants and Seiberg-Witten theory, Talk at Oberwolfach, Germany, June 1998.
o Froyshov invariants of Brieskorn homology spheres, Colloquim talk at the University of Notre Dame, South Bend, Indiana, Feb. 1998.
o Froyshov invariants of Brieskorn homology spheres, Seminar talk at the University of Michigan, Ann Arbor, Michigan, Feb. 1998.
o Seiberg-Witten equations and Seifert manifolds, Colloquim talk, IUPUI, Jan. 1998.
o Seiberg-Witten equations and Seifert manifolds, Colloquim talk, University of Florida, Gainesville, Jan. 1998.
o Seiberg-Witten invariants of homology spheres, Seminar talk at Pennsylvania State University, Dec. 1997.
o Froyshov invariants of Brieskorn homology spheres, Seminar talk at the Western Ontario University, London, Ontario, Dec. 1997.
o Froyshov invariants of Brieskorn homology spheres, Seminar talk at the Michigan State Univ., Nov. 1997.
o Finite energy Seiberg-Witten moduli spaces, Talk at the Ontario Topology Seminar, Fields Institute, Toronto, Oct. 1997.
o Eta invariants of Dirac operators on collapsing circle bundles over Riemann surfaces, Talk at the A.M.S. Meeting, Montreal, Sep. 1997.
o Adiabatic limits of the 3-dimensional Seiberg-Witten equations, Seminar talk at Northwestern University, Feb. 1997.
o Adiabatic limits of the Seiberg-Witten equations on Seifert manifolds, Talk at the A.M.S. Meeting, Pasadena, CA, Nov. 1996.
o Adiabatic limits of the Seiberg-Witten equations on Seifert manifolds, Seminar talk, Michigan State University, Oct. 1996.
o Gluing formulae for the index of families of Dirac operators, Talk at the A.M.S. Meeting, Orlando, FLA, Jan. 1996.
o The spectral flow, the Maslov index and decompositions of manifolds, Seminar talk at the Ohio University, Athens Ohio, April 1995.
o The spectral flow, the Maslov index and decompositions of manifolds, Seminar talk at the University of Texas at Austin, Nov. 1994.
o The index of families of boundary value problems, 1 hour talk at the Miniconference on index theory, Oct. 1994, IUPUI Indianapolis.
o The index of families of boundary value problems, Colloquium addresses at the Humboldt University in Berlin and Augsburg University (Germany), May 1994.
o The spectral flowm the Maslov index and decompostions of manifolds, Seminar talk, University of Michigan, Dec. 1993.
o The spectral flow, the Maslov index and decompositions of manifolds, Talk at the Workshop on Differential Geometry, Fields Institute, Waterloo, Ontario, Aug., 1993.
- The spectral flow, the Maslov index and decompositions of manifolds, Seminar lectures at Indiana University, Bloomington and IUPUI Indianapolis, April 1993.