I am retired now!
I was told by the Chair(s) that my teaching load
will be 5 to 6 undergraduate courses per year for the
rest of my carreer. Most of these courses will be
"service courses"(nothing related to my research areas)
mainly for nonmath students. The teaching load
distribution is very uneven at McMaster. It is
definitely not a level playing field (teaching should be
a "privilege" and not a "punishment", in my opinion).
This is the main reason I quit my "day job" as a
"teaching prof". I am retired as of July 1st, 2015, but
I hope that wouldn't change the fact that I am still a
mathematcian!
Currently, I am trying to work on the
following problems:
1. Properties of Large Scale Networks and Graphs
2. Efficient Manifold Learning Algorithms
3. Asymptotic properties of Heat Kernels
4. Implementing geometric ideas
in Probability and Statistics
I have been teaching 4 to 5 undergraduate courses a year
(instead of the usual 3 courses for "ordinary" profs and
2 for "named chairs") for the last 10 years without any
research leaves (sabbaticals) and this is rather unusual
for someone with my seniority and with
what I think was a fairly reasonable track record of
doing research. Over the course of 30 years at McMaster
I have supported many a young postdoc (three of them
are prominent members of my department, including the
present Chairman of the department). These things
obviously don't count a lot at McMaster and for some
strange administrative reason
(selective institutional memory), I am no longer
regarded as a "research professor" in the department.
The department views me as a "teaching professor" (sic)
and there has been almost zero support for the kind of
research I used to do (differential geometry). For
example, I am not allowed to teach graduate courses
anymore and most of the courses I have to teach are not
even for students in Mathematics. I now consider my
research more or less a "pleasant hobby", that I pursue
during my spare time.
Here is a bit of history!
My research is not a burden for the
taxpayer anymore, since it is no longer supported
(for 4 years now) by any funding agency
(public or private) and that was the reason given by
the University administration for denying me any
"research leaves a.k.a. sabbaticals", so I have been
busy teaching every semester for the last 9 years.
I was told by my Chairman (a former postdoc of mine)
that my teaching load is 5 to 6 undergraduate courses
every year until I retire.
My last sabbatical was in 2005/06, ten years
ago, and the last time I taught a graduate
course in my area of expertise was in
2010/11, five years ago. These are the main
reasons I gave up doing any research in
differential geometry and became more
interested in other areas of research. At
McMaster very few people understand or
appreciate, let alone support the research I
do (or did).
Nevertheless, I funded "my" last postdoc in 2012, the
year my research leave was denied, not to
mention the numerous postdocs of my esteemed
colleagues that I helped fund with my meager little
research grant for years and years before that (as
one of my colleagues told me afterwards: "a good
deed never goes unpunished")
There
was a lot of pressure in my department to be a
good citizen (gentlemen=agreemen(t)?) and fund
postdocs of a few "big shots" with much
bigger grants, with lighter teaching loads,
with named chairs, who get most of the credit
from the "system" (some of them even sitting
on NSERC committees, go figure!). Many of the
postdocs that I funded didn't understand any
of my research and some postdocs and graduate
students didn't even know that I was funding
them (NSERC should know though, because that's
against their own bureaucratic rules of how
taxpayer's money is spent, but people like to
bend rules when it's convenient for them). Oh
well, some of these young ambitious guys
became successful researchers and/or
administrators in due course, so it doesn't
really matter that much to them anymore
BUT just for the
record here is a sample of highly successful
postdoctoral fellows that I
cosupervised and partially supported
with my NSERC research grant over the past twentyfive
years. Of course, I am very honoured and proud
to be partially(sic) involved with these wonderfully
talented people at the beginning of their successful
careers, a lot more successful than mine, who
hopefully are enjoying their welldeserved
sabbaticals, substantial research grants and important
administrative positions (all because they didn't read
any of my papers? what an irony LOL)
 Hans U. Boden (Professor and Chair of Math
& Stats at McMaster)
 Miroslav Lovric (Professor and Associate
Chair of Math & Stats at McMaster)
 Mattheus Grasselli (Associate Professor
and DeputyDirector, Fields Institute)
 Liviu Nicolaescu (Professor,
University of Notre Dame)
 Christoph Böhm (Professor,
University of Münster)
 Igor Belagradek (Professor, Georgia
Tech)
 Tahir Choulli (Associate Professor,
University of Alberta)
 Virginie Charette (Professor, University
of Sherbrooke)
 XiuXong Chen (Professor, University
of Wisconsin)
 Eduardo MartinezPedroza (Assistant
Professor, Memorial University)
 Marianty Ionel (Professor Adjunto,
Univ. Fed., Rio de Janeiro)

Alain Bourget (Associate Professor,
California State University, Fullerton)
 Vincent Bonini (Assistant Professor,
California Polytechnic State University)
 Ergun Yalcin (Professor, Bilkent
University, Turkey, Hooker visiting profesor)
Because a prominent (wellfunded and
wellconnected) colleague from McGill asked, let me
explain that I did not mention Spiro Karigiannis
(Associate Professor, University of Waterloo) in the
above list because, being a Canadian, he came with his
own NSERC funding and although I did work with him
(and consequently he did read some of my
papers!) It is a rather touchy
issue in my department who is allowed to be called
"the supervisor", especially of successful postdocs.
Some "big shots" want to get all the HQP numbers,
important for research metrics used by beancounters.
Differential Geometry
Mathematical Physics
Publications and Preprints
Differential
Geometry
WHY DO I STUDY
DIFFERENTIAL GEOMETRY ?
Geometry is one of the oldest disciplines of Science and
dates back to ancient times. The Egyptians used
geometric formulas to measure the land, whence the Greek
word: geometry. The Greeks themselves adored the subject
and cultivated it into a beautiful abstract piece of
Mathematics, as epitomized in Euclid's books, which
still remain for most of us the first, and
unfortunately, for many, the last encounter with the
subject.
Modern Differential Geometry began with Gauss' work on
the Theory of Surfaces in the early 19th century. Gauss
was again partly motivated by practical surveying
problems about mapping the surface of the earth. By that
time it was well known that the earth is not flat and
hence that Euclidean Geometry is not adequate. Gauss
applied the powerful method of the Infinitesimal
Calculus, invented about a century earlier by Newton and
Leibniz, in his investigations on the curvature of
surfaces. A few decades later this Gaussian theory was
generalized to a higher level of abstraction and
dimension by Riemann, who introduced the notion of a
manifold as an appropriate form of space where one can
study geometries. Euclidean geometry then became just
one very special case among an infinity of possible
geometries and the laws of Euclidean geometry were
postulated to be true only for measurements at a very
small scale, to be precise, at the infinitesimal level.
These Euclidean measurements, in other words, the
metric, is now allowed to vary from one point to the
next. The idea of space itself as a dynamic entity was
born.
It was the genius of Einstein who realized that these
new geometric ideas should be the basis for
understanding not just the shape of the earth but that
of the while universe of space and time. His
revolutionary General Theory of Relativity is a
masterpiece of Geometric Physics explaining that
mysterious fundamental force of Nature, Gravitation,
which holds the universe together on a large scale, as a
manifestation of the curvature of spacetime itself. In
order to formulate this theory, Einstein relied on the
differentialgeometric calculus developed by Gauss,
Riemann, Christoffel, Ricci and LeviCivita. In his
later years Einstein dreamed of generalizing his theory
to encompass all the other known forces of Nature. This
dream, known as the GUT (Grand Unified Theory), is still
pursued by theoretical physicists and over the last
three decades, there has been some spectacular new
theoretical advances, which might ultimately become
important stepping stones to a GUT. Most of these
theories such as Gauge Theory, String Theory, Mtheory
etc., are in fact very geometrical and have strong
dialectical interactions with recent advances in Pure
Mathematics, especially in Geometry and Topology. One
basic idea of these new physical theories is to extend
the arena of physics from the 4dimensional spacetime
of Relativity to a higher dimensional manifold (say of
dimension 10 or 11), to incorporate all the degrees of
internal freedoms and symmetries that are needed to
explain all the other forces of nature. The other
fundamentally new point of view is to treat particles
and the forces between them not just through points and
lines but by using higher dimensional strings and
menbranes in order to resolve the basic contradiction
between General Relativity and Quantum Mechanics. The
laws of nature should then be described (at least at an
approximate level) by field equations involving some
form of curvature and reflecting all the inherent
(super)symmetries. Curvature, in its various
manifestations, is the fundamental invariant of
Differential Geometry. It is calculated locally by means
of the Infinitesimal Calculus but it governs, on a
broader scale, the global shape and size of the whole
space leading to a fascinating interplay between
geometry, topology and analysis. For example Einstein's
theory is governed by a single field equation relating
the Ricci curvature to the stressenergy tensor.
My own research in this vast field of Differential
Geometry is centered around the problem of deforming
curvature and investigating its stability properties
under perturbations. I have worked on deformation
problems associated to solving the Riemannian version of
Einstein's equation and also on rigidity problems for
the scalar curvature arising from the spinorial proof
given by E.Witten for the Positive Mass Theorem in
General Relativity. Recently, there has been a lot of
activity in theoretical physics on the geometry of black
holes, which bears some relation to the mathematical
results that I was investigating. I have also became
interested in using differential geometric methods in
problems arising in probability and statistics, in
particular, understanding statistical and quantum
features of mechanical and geometrical problems in the
large dimensional limit.
In conclusion, I would like to point out that in spite
of its fascinating and intriguing relationship to
Physics, Differential Geometry is a purely mathematical
discipline, which can be pursued in its own right. It is
certainly a very active and promising area of
mathematical research with many important and
interesting developments during the last 50 years. It is
also a subject which interacts with many other branches
of Mathematics. At an elementary level, it is based only
on Calculus and Linear Algebra, the 2 basic Mathematics
courses taught during the first 2 years at any
University.
Mathematical Physics
I began to become interested in mathematics at a young
age when I discovered that this was the language of
the universe. My "Jugendtraum" was really to
understand physics and astronomy. I feel lucky that my
main research area, differential geometry is the main
"lingua franca" of physics. Presently, I am working on
calibrated cycles in manifolds with special holonomy,
problems that show up in string theory and Mtheory in
theoretical physics. My "Alterstraum" is now to
understand the AdS/CFT correspondence, in particular
mirror symmetry and the intriguing relationship
between analytic number theory and theoretical
physics.
FOR A SHORT INFORMAL INTRODUCTION TO GENERAL
RELATIVITY BY JOHN (not Joan) BAEZ CLICK
HERE
Publications
and Preprints
LIST OF PUBLICATIONS
MinOo: Krümmung und differenzierbare Struktur auf
reellprojektiven Räumen; Diplom Arbeit,
Bonn (1973)
MinOo: Krümmung und differenzierbare Struktur auf
komplexprojektiven Räumen; Bonner Math. Schriften,
vol.93, (1977).
MinOo and E.A.Ruh: Comparison theorems for compact
symmetric spaces ; Ann. Sci. Ec. Norm. Sup.
t.12 (1979), p.335353.. pdffile
MinOo and E.A.Ruh: Vanishing theorems and almost
symmetric spaces of noncompact type ; Math. Ann.
257 (1981), p. 419443. pdffile
MinOo: An L2Isolation Theorem for YangMill
fields ; Comp. Math. 47.2 (1982), p.153163.
J.Dodziuk and MinOo: An L
2Isolation Theorem for YangMills fields over
complete manifolds ; Comp. Math 47.2 (1982), p.16516.
MinOo: YangMills fields and the isoperimetric
inequality; in Global Riemannian Geometry
(Durham), E.Horwood Ltd.(1984).
MinOo: Maps of minimum energy from compact
simplyconnected Lie groups ; Ann.Global Anal.
& Geom. 2(1984), p.119128.
J.Bemelmans, MinOo and E.A.Ruh:
Smoothing Riemannian metrics ; Math. Z. 188 (1984),
p.6974. pdffile
MinOo: Integrabilitaet geometrischer Strukturen vom
halbeinfachen Typ ; Habilitationsschrift,
Bonn(1984).
MinOo and E.A.Ruh: An integrability condition for
semisimple Lie groups ; in Diff.Geom. &
Complex Analysis, (Rauch memorial vol.) Springer
(1985).
M.MinOo: Spectral rigidity for manifolds wit
negative curvature operator ; Contemp. Math.,
vol.51 (1985) AMS, Providence
M.MinOo and E.A.Ruh: Curvature deformations ;
Proc.Katata(Japan), Lect.Notes in Math. vol.1201,
Springer (1985).
M.MinOo: Almost symmetric spaces ; Asterisque,
vol. 163164 (1988), p.221246.
M.MinOo: Scalar curvature rigidity of asymptotically
hyperbolic spin manifolds ; Math. Ann. vol.285
(1989), p.527539. pdffile
M.MinOo and E.A.Ruh: L2 curvature pinching ;Comment.
Helv. Math. vol.65 (1990), p.3651. pdffile
M.MinOo: Almost Einstein manifolds of negative Ricci
curvature ; J. Diff. Geom. vol. 32 (1990), p.457472.
P.Ghanaat, M.MinOo and E.A.Ruh: Local structure of
Riemannian manifolds ; Indiana Univ. J. Math.,
vol.39.4 (1990) p.13051312. pdffile
M.MinOo, E.A.Ruh and P.Tondeur: Vanishing theorems
for the basic cohomology of Riemannian foliations
; J. reine u. ang. Math., vol. 415
(1991), p.167174. pdffile
M.MinOo, E.A.Ruh and P.Tondeur: A comparison theorem
for almost Lie foliations ; Ann. Global Anal.
& Geom., vol. 9.1 (1991), p.6166.
M.MinOo, E.A.Ruh and P.Tondeur: Transversal curvature
and tautness for Riemannian foliations; Lect.
Notes in Math. vol.1481, p.145146, Springer (1991).
J.Escobar, A.Freire and M.MinOo: L2 vanishing
theorems in positive curvature ; Indiana Univ. J.
Math, vol.42.4 (1993) p.15451554. pdffile
P.March, M.MinOo, and E.A.Ruh: Mean Curvature of
Riemannian Foliations ; Canadian Math.
Bull. 39.1 (1996), p.95105.
M. MinOo: Scalar curvature rigidity of certain
symmetric spaces ; Geometry, topology, and
dynamics (Montreal),p. 127136, CRM Proc. Lecture
Notes, 15, A. M. S.,1998. pdffile
M.Lovric, M.MinOo and E.A.Ruh: Multivariate normal
distributions parametrized as a Riemannian
symmetric space; J. Multivariate Analysis,
vol.74.1 (2000), pp. 36  48. pdffile
M.Lovric, M.MinOo and E.A.Ruh: Deforming transversal
Riemannian metrics of foliations ; Asian J. of
Math., vol. 4.2 (2000), pp. 303  314. pdffile
M.MinOo and J. A. Toth: The Levy
concentration phenomenon for special functions on
rankone symmetric spaces ; Methods
and Applications of Analysis, vol. 7.1
(2000), p. 151  164. pdffile
A. Bourget, D. Jakobson, M.MinOo and J. A.
Toth: A Law of large numbers for the zeros of
HeineStieltjes polynomials ; Letters of Mathematical
Physics, vol. 64.2 (2003), p. 105 118. pdffile
M. MinOo: Dirac Operator in Geometry and Physics in
Global Riemannian Geometry: Curvature and Topology;
Advanced courses in Mathematics, CRM Barcelona,
Birkhauser (2003). pdffile
M. Ionel, S. Karigiannis and M.
MinOo: Bundle constructions of calibrated
submanifolds in R^7 anf R^8; Mathematical Research
Letters, vol. 12.4 (2005) pp. 493  512 . pdffile
S. Karigiannis and M. MinOo:
Calibrated subbundles in noncompact manifolds of
special holonomy; Annals of Global Analysis and
Geometry, vol. 28 (2005) pp. 371  394. pdffile
H. Davaux and M. MinOo:
VafaWitten bound on the complexprojective
space, Annals of
Global Analysis and Geometry, vol.30 (2006) pp. 29 
36. pdffile
M. Ionel and M. MinOo:
Cohomogeneity one special lagrangian submanifolds in
the deformed and resolved conifolds, Illinois J.
Math., vol. 52.3 (2008), pp 839  865. pdffile
G. Fan, M. MinOo and G.S.K.
Wolkowicz: "Hopf bifurcation of delay differential
equations with delay dependent parameters", Canadian
Appl. Math. Quaterly, vol. 17.1 (2009), pp
3760. pdffile
M. MinOo: "An integrability
condition for simple Lie groups II" SIGMA 11 (2015)
http://www.emis.de/journals/SIGMA/2015/027/
PREPRINTS
A. Kolly, M. MinOo and E.A.
Ruh: The GaussBonnetChern Theorem (1999)
D. Egloff and M. MinOo: Convergence of Monte
Carlo algorithms for pricing American Options (2002). pdffile
M. Ionel and M. MinOo: Cohomogeneity one special
lagrangian submanifolds in the deformed
conifold (2005) pdffile
M. Ionel and M. MinOo: Special
Lagrangians of cohomogeneity one in the resolved
conifold (2005) pdffile
M. MinOo: Interacting Markov chains
on undirected networks (2014) pdffile