The lectures cover perverse sheaves and the topology of algebraic varieties, an introduction to affine Grassmannians and the geometric Satake equivalence, Springer theories and orbital integrals, perverse sheaves and fundamental lemmas,

K-theory computations in enumerative geometry, and perverse sheaves on instanton moduli spaces.

In [12] and [14], Lascoux and Schutzenberger introduced (double) Grothendieck polynomials indexed by permutations as representatives of

K-theory classes of structure sheaves of Schubert varieties in a full flag variety.

The first, developed mainly by Bloch, Kato, and Tsuji, uses algebraic

K-theory, syntomic complexes, and p-adic vanishing cycles, while the second, more in line with Tate~s original ideas, was developed by Faltings using his almost mathematics and purity theorems.

Is the uncertain theory,

K-theory [10]solve the recent intriguing statistical problems by the power of this Neutrosophic logic ?

KS1] Gennadi Kasparov, Georges Skandalis, Groups acting on buildings, operator

K-theory, and Novikov's conjecture,

K-Theory 4 (1991), no.

Eleven contributions are selected from the eight working groups in the areas of elliptic surfaces and the Mahler measure, analytic number theory, number theory in functions fields and algebraic geometry over finite fields, arithmetic algebraic geometry,

K-theory and algebraic number theory, arithmetic geometry, modular forms, and arithmetic intersection theory.

The analogue of positivity in equivariant

K-theory was (again, abstractly) proven in Anderson et al.

7: Correlation plots of SW-model estimated versus observed daily transpiration for rain, non-rain and all weather conditions in the Mengcha village study area However, the SW-model is essentially derived from the PM-model and both are based on the

K-theory.

But Nicusor Dan, a mathematician who graduated from the Sorbonne University in Paris, decided to fight back - even if this meant spending less time on his cherished research about polylogarithms and the

K-theory at the Romanian Institute for Mathematics.

Among the topics are the functoriality of Rieffel's generalized fixed-point algebras for proper actions, division algebras and supersymmetry, Riemann-Roch and index formulae in twisted

K-theory, noncommutative Yang-Mills theory for quantum Heisenberg manifolds, distances between matrix algebras that converge to coadjoint orbits, and geometric and topological structures related to M-branes.

We will now use Theorem 6 to compute the

K-theory of [D.

Cibotaru, Daniel, University of Notre Dame, Localization formulae in odd

K-theory.