CV
Publications
Talks&Lectures
Date of birth: Dec. 24, 1964, Iasi, Romania
B.S and M.S in Mathematics: 1987, Al.I.Cuza University of Iasi, Romania .
PhD in Mathematics: 1994, Michigan State University, USA.
Thesis advisor: Professor Thomas H. Parker.
·
``Gheorghe Tzitzeica'' Prize of the Romanian
Academy of Sciences, 1996 for the paper ``Rigidity of generalized Laplacians
and some geometric applications''.
·
NSF Grant DMS-0071820, 2000-2003.
·
NSF Grant DMS-0303601, 2003-2006
Associate Professor , University of Notre Dame, 2002-
Visiting scholar,_ _Fourier Institute, Grenoble,
France, May-June 2003.
Visiting scholar, The Ohio State University, Fall 2001.
Assistant Professor, University of Notre Dame, 1998-2002 .
Postdoctoral Fellow, Mc Master University, Ontario, Canada,
1997-1998
Assistant Professor, University of Michigan,
1994 -1997.
Visiting scholar, Humboldt University, Berlin, Germany, May
1994.
Teaching Assistant, Michigan State University, 1990-1994.
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
57. _On
the_ total curvature of semialgebraic_ graphs_ arXiv: 0806.3683 We define the total
curvature of a semialgebraic graph $\Gamma\subset \bR^3$ 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 (tame) sets are the pfaffian sets introduced
by Khovanski, and a flow $\Phi: \mathbb{R}\times X\rightarrow X$ on pfaffian set $X$ is tame if the graph of $\Phi$ is a pfaffian subset of
$\mathbb{R}\times X\times X$. Any compact tame
set admits plenty tame flows. We prove that the flow determined by the gradient of a generic real analytic function with respect to a generic real analytic metric is tame. The typical tame gradient flow satisfies the Morse-Smale condition, and we prove that in the tame context, under certain spectral constraints, the Morse-Smale condition implies the
fact that the stratification by
unstable manifolds is Verdier and
Whitney regular. We explain how to compute the Conley indices of isolated stationary points of tame flows in
terms of their unstable varieties, and then give a complete classification of
gradient like tame flows with finitely many stationary points. We use this technology to produce a Morse theory on posets generalizing R. Forman's discrete Morse theory. Finally, we
use the Harvey-Lawson
finite volume flow 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. Also, you can watch Arnold talking
about this.
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 Budapest semester in math that I learned
from_ A. Stipsicz.__ I suspect somebody else__ has thought of this
generalization before, but in any case, here it is.____
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 Grenoble.
34._ Notes on the topology of complex singularities , (PDF, Revised 07/11/2001) This is an ongoing process. I have included lots of NEW examples.
33.__ Mixed Hodge structures
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
4. Localization
formulae in odd K-theory, This is the
PhD dissertation of Daniel Cibotaru. I like
very much how it turned out, and I am sure it will find applications.
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
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", Ohio State University, March 28-30, 2002
o
Seiberg-Witten invariants
of rational homology 3-spheres, Seminar
talk at McMaster University, March 11, 2002.
o
Seiberg-Witten invariants
and isolated surface singularities, (audio
file) Lecture
at the Symposium
on Analysis and Geometry, Fields Institute, Toronto, March 9-10,
2002.
o
Gauge theoretic
invariants of rational homology spheres, Seminar talk at the Ohio State University, Oct. 8-9, 2001.
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,
March 2-3 2001
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.