Things that I wrote

I've grouped my writings  into several categories

• Papers 
• Varia (mini surveys and papers I may never publish)
• Books and  notes

Papers

1. Critical points of multidimensional random Fourier series: central limits,    arXiv: 1511.04965, to appear in Bernoulli, I prove that the number of critical points of a random Fourier series on $\mathbb{R}^n/(L\mathbb{Z})^n$  satisfies a central limit theorem as $L\to\infty$.
2. A CLT involving  critical points of  random smooth functions on an Euclidean space,  arXiv: 1509.06200, to appear in Stoch Proc. and Appl.  I show that the number  of critical points of an isotropic Gaussian random function inside a cube in $\mathbb{R}^n$ satisfies  satisfies a central limit theorem as the size of the cube increases indefinitely.

Varia

Books and notes

1. Wiener chaos and limit theorems,  I survey the concepts of Gaussian Hilbert spaces, their chaos decomposition and the accompanying Malliavin calculus. I then describe how these ingredients fit in the recent central limit theorems of Nourdin and Peccati in the Wiener chaos context.  
2. The wave group and spectral geometry,   I describe in some detail Hadamard's    construction of  parametrix for the wave operator on a Riemann manifold and then explain how to use this for spectral estimates. I follow Hormander's modern approach.
3. Pseudodifferential operators and  some geometric  applications,  These are notes for a graduate course I've taught at the  University of Notre Dame in Spring 2010.
4. The signature theorem and some of its applications,  These are notes for the  Topics in Topology class I taught during Fall 2008.  I cover  most of the prerequisite required to understand  Hirzebruch's signature  theorem and Milnor's construction of exotic spheres. 
5. Microlocal investigations of shape, Notes for a topics class, Notre Dame Fall 2006.
6. Notes on Morse Theory, Notes for a topics class, Notre Dame Fall 2005. (This is the 2nd edition of my Morse theory book, with any new corrections incorporated.)
7. Notes on the Atiyah-Singer index theorem, Notes for a topics class  Notre Dame, Spring 2004 and 2013.
8. The Poincare-Verdier duality, These are notes about the derived category of sheaves and what you can do with it. 
9. Notes on the Reidemeister Torsion,   This is more or less my  Walter de Gruyter book with the sam name. I'm particularly proud of   chapter 3 in this book where I explain how to compute  the torsion of certaion classes of 3-manifolds using  Fourier transform on discrete Abelian groups
10. Notes on the Topology of Complex Singularities,  Notes  that grew from a  topic  course at Notre Dame  1999-2000.
11. Notes on Seiberg-Witten theory, These grew up from a seminar I ran at McMaster 1997-98 and a topic course at  the university of Notre Dame 1998-99.
12. Lectures on the Geometry of Manifolds,   This is my first book, and the one I'm most proud of, although it suffers from  youthful exuberance. This   is  more polished than the published version.
13. Introduction to Real Analysis,    These are  notes for the four-semester honors calculus at the University of Notre Dame. It covers  the differential  and integral calculus of functions of   one and several variables, proofs included. I also   discuss a few topological concepts.
14. Introduction to Probability,  These are notes for the undergraduate probability class I've been teaching at the university of Notre Dame.
15. Notes on Linear Algebra,  These are notes for  an  Honors Linear Algebra course at Notre Dame, Spring 2013.