[MD-sorular] Alain Lascoux, Öklid Algoritması Çalıştayı, 5-12 Şubat 2012, NMK

Kürsat Aker kursataker at gmail.com
23 Eki 2011 Paz 01:04:42 EEST


Euclid algorithm, Continuous Fractions, Dyck Paths
Eğitmen: Prof. Alain Lascoux
Kurum: Institut Gaspard Monge, Universite Paris-Est
Seviye: Beginning Undergraduate
Önkoşul: The notion of a determinant. Some knowledge about
symmetric functions is preferable, but necessary notions will be recalled .
Kaynak: Derste kullanılacak notlar için tıklayın.
Tarihler: 6 - 12 Şubat 2012
İçerik: It is classical that continuous fractions, rational
approximations of functions of
one variable, orthogonal polynomials, are all related to the Euclidean division
of polynomials and to the combinatorics of Dyck and Motzkin paths. I shall show
that the theory of symmetric functions allows to handle easily the different
determinants arising in these theories, and give as well their combinatorial
descriptions in terms of paths.


Cebir ve Kombinatorik için Bilgisayar
Eğitmen: Dr. Kürşat Aker
Kurum: İstanbul Bilgi Üniversitesi
Seviye: Graduate, advanced undergraduate, beginning undergraduate, high school
Önkoşul: -
Kaynak: http://phalanstere.univ-mlv.fr/~ace/ACE/3.0/manual.html
Tarihler: 5 - 12 Şubat 2012
İçerik: Bu derste, özellikle Maple, ACE ve Sage kullanarak, Prof.
Lascoux'nun derslerinde sözü
geçen hesapları bilgisayar kullanarak nasıl yapabileceğimizi işleyeceğiz.


A Survey on Thom Polynomials
Eğitmen: Yard. Doç. Özer Öztürk
Kurum: MSGSÜ
Seviye: Advanced undergraduate, graduate
Önkoşul: -
Kaynak: -
Tarihler: 5 - 6 Şubat 2012
İçerik: We shall discuss different methods of computations of the Thom
polynomials of singularity classes of mappings. We shall mainly focus on
methods developed in the last decade. We shall give detailed computations of
Thom polynomials with a focus on their expansions in the basis of Schur
functions.
Kaynakça:
1. A. Du Plessis, C.T.C. Wall, The geometry of topological stability,
Oxford Math. Monographs, 1995.
2. L. Fehér, R. Rimányi,Thom series of contact singularities, math.
AG/0809.2925v2.
3. A. Lascoux, Symmetric functions and combinatorial operators on polynomials,
CBMS/AMS Lectures Notes 99, Providence (2003).
4. A. Lascoux, P. Pragacz, Thom polynomials and Schur functions: the
singularities
A_3(-), Publ. RIMS Kyoto Univ. 46 (2010), 183-200.
5. Ö. Öztürk, Thom polynomials and Schur functions: the singularities
$III_{2,3}$, Ann.
Polon. Math. 99 (2010), 295-304.
6. P. Pragacz, Thom polynomials and Schur functions: the singularities
$I_{2,2}(-)$,
Ann. Inst. Fourier (2007), 1487--1508.
7. P. Pragacz, A. Weber, Positivity of Schur function expansions of
Thom polynomials,
Fund. Math. 195 (2007), 85--95.
8. R. Rim\'anyi,Thom polynomials, symmetries and incidences of
singularities, Inv.
Math. 143 (2001), 499--521.
9. R. Thom, Les singularit\'es des applications différentiables, Ann.
Inst. Fourier (1955--56),
43--87.


Applications of Schubert, Grothendieck, Key Polynomials
Eğitmen: Yard. Doç. Nesrin Tutaş
Kurum: Akdeniz Ü.
Seviye: Graduate
Önkoşul: -
Kaynak: -
Tarihler: 6- 10 Şubat 2012
İçerik: We will give some examples and applications of Schubert,
Grothendieck,Key
polynomials.
Kaynakça:
1. A.Lascoux, lecture notes, polynomials.
2. Hiller, Geometry of Coxeter Groups.
3. Brion, Lectures on the Geometry of Flag Varieties:
http://arxiv.org/abs/math/0410240
4. J. Bernstein, I.M. Gelfand, S.I. Gelfand Schubert cells and
cohomologies of spaces G/P. Uspekhi Mat. Nauk 38, No.3, 3-26(1973).
  http://www.math.tau.ac.il/~bernstei/Publication_list/publication_texts/BGG-CoxeterF-Usp.pdf
5. Fulton, Young Tableaux
6. Vogan, Geometry of Flag Manifolds and Representation Theory:
http://www-math.mit.edu/~dav/flags.pdf


2011/10/21 Kürsat Aker <kursataker at gmail.com>:
> Alain Lascoux, Öklid Algoritması Çalıştayı, 5-12 Şubat 2012, NMK
>
> http://matematikkoyu.org/tr/oklid_calistay
>


MD-sorular mesaj listesiyle ilgili daha fazla bilgi