| Preface |
| Notes on the Life and Work of Alexander Grothendieck / Piotr Pragacz |
| References |
| Characteristic Classes of Singular Varieties / Paolo Aluffi |
| Lecture I / 1： |
| Lecture II / 2： |
| Lecture III / 3： |
| Lecture IV / 4： |
| Lecture V / 5： |
| Lectures on the Geometry of Flag Varieties / Michel Brion |
| Introduction |
| Grassmannians and flag varieties |
| Singularities of Schubert varieties |
| The diagonal of a flag variety |
| Positivity in the Grothendieck group of the flag variety |
| Combinatorial K-theory / Anders Skovsted Buch |
| K-theory of Grassmannians |
| The bialgebra of stable Grothendieck polynomials |
| Geometric specializations of stable Grothendieck polynomials |
| Degeneracy loci |
| Grothendieck polynomials / 6： |
| Alternating signs of the coefficients c[subscript omega,mu] / 7： |
| Morse Functions and Cohomology of Homogeneous Spaces / Haibao Duan |
| Computing homology: a classical method |
| Elements of Morse theory |
| Morse functions via Euclidean geometry |
| Morse functions of Bott-Samelson type |
| Integrable Systems and Gromov-Witten Theory / Ali Ulas Ozgur Kisisel |
| Completely integrable systems |
| Random matrices and enumeration of graphs |
| Witten's conjecture and Kontsevich's solution |
| Some of the further developments |
| Multiplying Schubert Classes |
| Characteristic map and BGG-operators |
| Structure constants for Schubert classes |
| A combinatorial proof of the Pieri formula |
| Lectures on Characteristic Classes of Constructible Functions / Jorg Schurmann |
| History |
| Calculus of constructible functions |
| Stratified Morse theory for constructible functions and Lagrangian cycles |
| Characteristic classes of Lagrangian cycles |
| Verdier-Riemann-Roch theorem and Milnor classes |
| Appendix: Two letters of J. Schurmann |
| Algebraic K-theory of Schemes / Marek Szyjewski |
| Grothendieck groups |
| K-theory of fields |
| Quillen Q-construction |
| [characters not reproducible] of noetherian schemes |
| [characters not reproducible] of certain varieties |
| Applications |
| Gromov-Witten Invariants and Quantum Cohomology of Grassmannians / Harry Tamvakis |
| Lecture One |
| Lecture Two |
| Lecture Three |
| Lecture Four |
| Lecture Five |
| Preface |
| Notes on the Life and Work of Alexander Grothendieck / Piotr Pragacz |
| References |
| Characteristic Classes of Singular Varieties / Paolo Aluffi |
| Lecture I / 1： |
| Lecture II / 2： |
