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 non-math 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 post-doc (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 tax-payer 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 post-doc 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 post-doc in 2012, the year my research leave was denied, not to mention the numerous post-docs 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 post-docs 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 post-docs that I funded didn't understand any of my research and some post-docs 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 post-doctoral fellows  that I co-supervised and partially supported with my NSERC research grant over the past twenty-five 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 well-deserved 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 Deputy-Director, 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)
  • Xiu-Xong Chen  (Professor, University of Wisconsin)
  • Eduardo Martinez-Pedroza (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 (well-funded and well-connected) 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 post-docs. Some "big shots" want to get all the HQP numbers, important for research metrics used by bean-counters.

Differential Geometry

Mathematical Physics

Publications and Preprints

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 space-time itself. In order to formulate this theory, Einstein relied on the differential-geometric calculus developed by Gauss, Riemann, Christoffel, Ricci and Levi-Civita. 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, M-theory 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 4-dimensional space-time 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 stress-energy 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 M-theory 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.


Publications and Preprints


Min-Oo: Krümmung und differenzierbare Struktur auf reell-projektiven Räumen; Diplom Arbeit, Bonn (1973)

Min-Oo: Krümmung und differenzierbare Struktur auf komplex-projektiven Räumen; Bonner Math. Schriften, vol.93, (1977).

Min-Oo and E.A.Ruh: Comparison theorems for compact symmetric spaces ; Ann. Sci. Ec. Norm. Sup. t.12 (1979), p.335-353.. pdf-file

Min-Oo and E.A.Ruh: Vanishing theorems and almost symmetric spaces of non-compact type ; Math. Ann. 257 (1981), p. 419-443. pdf-file

Min-Oo: An L2-Isolation Theorem for Yang-Mill fields ; Comp. Math. 47.2 (1982), p.153-163.

J.Dodziuk and Min-Oo: An L 2-Isolation Theorem for Yang-Mills fields over complete manifolds ; Comp. Math 47.2 (1982), p.165-16.

Min-Oo: Yang-Mills fields and the isoperimetric inequality; in Global Riemannian Geometry (Durham), E.Horwood Ltd.(1984).

Min-Oo: Maps of minimum energy from compact simply-connected Lie groups ; Ann.Global Anal. & Geom. 2(1984), p.119-128.

J.Bemelmans, Min-Oo and E.A.Ruh: Smoothing Riemannian metrics ; Math. Z. 188 (1984), p.69-74. pdf-file

Min-Oo: Integrabilitaet geometrischer Strukturen vom halb-einfachen Typ ; Habilitationsschrift, Bonn(1984).

Min-Oo and E.A.Ruh: An integrability condition for semi-simple Lie groups ; in Diff.Geom. & Complex Analysis, (Rauch memorial vol.) Springer (1985).

M.Min-Oo: Spectral rigidity for manifolds wit negative curvature operator ; Contemp. Math., vol.51 (1985) AMS, Providence

M.Min-Oo and E.A.Ruh: Curvature deformations ; Proc.Katata(Japan), Lect.Notes in Math. vol.1201, Springer (1985).

M.Min-Oo: Almost symmetric spaces ; Asterisque, vol. 163-164 (1988), p.221-246.

M.Min-Oo: Scalar curvature rigidity of asymptotically hyperbolic spin manifolds ; Math. Ann. vol.285 (1989), p.527-539. pdf-file

M.Min-Oo and E.A.Ruh: L2 -curvature pinching ;Comment. Helv. Math. vol.65 (1990), p.36-51. pdf-file

M.Min-Oo: Almost Einstein manifolds of negative Ricci curvature ; J. Diff. Geom. vol. 32 (1990), p.457-472.

P.Ghanaat, M.Min-Oo and E.A.Ruh: Local structure of Riemannian manifolds ; Indiana Univ. J. Math., vol.39.4 (1990) p.1305-1312. pdf-file

M.Min-Oo, E.A.Ruh and P.Tondeur: Vanishing theorems for the basic cohomology of Riemannian foliations ; J. reine u. ang. Math., vol. 415 (1991), p.167-174. pdf-file

M.Min-Oo, E.A.Ruh and P.Tondeur: A comparison theorem for almost Lie foliations ; Ann. Global Anal. & Geom., vol. 9.1 (1991), p.61-66.

M.Min-Oo, E.A.Ruh and P.Tondeur: Transversal curvature and tautness for Riemannian foliations;  Lect. Notes in Math. vol.1481, p.145-146, Springer (1991).

J.Escobar, A.Freire and M.Min-Oo: L2 vanishing theorems in positive curvature ; Indiana Univ. J. Math, vol.42.4 (1993) p.1545-1554. pdf-file

P.March, M.Min-Oo, and E.A.Ruh: Mean Curvature of Riemannian Foliations ; Canadian Math. Bull. 39.1 (1996), p.95-105.

M. Min-Oo: Scalar curvature rigidity of certain symmetric spaces ; Geometry, topology, and dynamics (Montreal),p. 127--136, CRM Proc. Lecture Notes, 15, A. M. S.,1998. pdf-file

M.Lovric, M.Min-Oo and E.A.Ruh: Multivariate normal distributions parametrized as a Riemannian symmetric space; J. Multivariate Analysis, vol.74.1 (2000), pp. 36 - 48. pdf-file

M.Lovric, M.Min-Oo and E.A.Ruh: Deforming transversal Riemannian metrics of foliations ; Asian J. of Math., vol. 4.2 (2000), pp. 303 - 314. pdf-file

M.Min-Oo and J. A. Toth: The Levy concentration phenomenon for special functions on rank-one symmetric spaces ; Methods and Applications of Analysis, vol. 7.1 (2000), p. 151 - 164. pdf-file

A. Bourget, D. Jakobson, M.Min-Oo and J. A. Toth: A Law of large numbers for the zeros of Heine-Stieltjes polynomials ; Letters of Mathematical Physics, vol. 64.2 (2003), p. 105 -118. pdf-file

M. Min-Oo: Dirac Operator in Geometry and Physics in Global Riemannian Geometry: Curvature and Topology; Advanced courses in Mathematics, CRM Barcelona, Birkhauser (2003). pdf-file

M. Ionel, S. Karigiannis and M. Min-Oo: Bundle constructions of calibrated submanifolds in R^7 anf R^8; Mathematical Research Letters, vol. 12.4 (2005) pp. 493 - 512 . pdf-file

S. Karigiannis and M. Min-Oo: Calibrated sub-bundles in non-compact manifolds of special holonomy;  Annals of Global Analysis and Geometry, vol. 28 (2005) pp. 371 - 394.   pdf-file

H. Davaux and M. Min-Oo: Vafa-Witten bound on the complex-projective space,  Annals of Global Analysis and Geometry, vol.30 (2006) pp. 29 - 36. pdf-file

M. Ionel and M. Min-Oo: Cohomogeneity one special lagrangian submanifolds in the deformed and resolved conifolds, Illinois J. Math., vol. 52.3 (2008), pp 839 - 865.  pdf-file

G. Fan, M. Min-Oo and G.S.K. Wolkowicz:  "Hopf bifurcation of delay differential equations with delay dependent parameters", Canadian Appl. Math. Quaterly, vol. 17.1 (2009), pp 37-60.  pdf-file

M. Min-Oo: "An integrability condition for simple Lie groups II" SIGMA 11 (2015)


A. Kolly, M. Min-Oo and E.A. Ruh:  The Gauss-Bonnet-Chern Theorem (1999)
D. Egloff and M. Min-Oo: Convergence of Monte Carlo algorithms for pricing American Options (2002). pdf-file

M. Ionel and M. Min-Oo: Cohomogeneity one special lagrangian submanifolds in the deformed conifold (2005) pdf-file

M. Ionel and M. Min-Oo: Special Lagrangians of cohomogeneity one in the resolved conifold (2005) pdf-file

 M. Min-Oo: Interacting Markov chains on undirected networks (2014)  pdf-file