IST - Polynomials (2022)

Speakers and Syllabus

 Mohali  Tutors:

  1. Kh.HerachandraSingh,ManipurUniversity

  2. RanjanBera,ISIBangalore

  3. SaranyaNair,BITSGoa

  4. H.Sharma,IITDelhi

  5. MahinshiSingla,JNUNewDelhi

  6. P.Yadav,ISIDelhi

 

Name of the speaker with Affiliation Number  of  lectures Detailed Syllabus
S.D.Adhikari,RKMVERI,Belur 4 Lectures of 1.5hrs each
  1.  Basic Definitions about polynomials and aTheorem of Gauss
  2.  Polynomials over Fields
  3.  GCD of polynomials
  4.  Polynomials with prescribed values
  5.  The resultant and discriminant
  6.   Algebraic numbers:Definition and main properties
  7.   Kronecker’s theorem and Liouville’s theorem
Shanta Laishram,ISI Delhi  8 Lectures of 1.5 hrs each
  1.  Newton polygons and Galois group
  2.  Cyclotomic Polynomials
  3.  Bernoulli polynomials
  4.  Chebyshev polynomials
  5.  Bessel Polynomials
  6.  Legendre Polynomials
  7.  Laguerre polynomials
  8.  0, 1 polynomials
  9.  Density results
B.Sury, ISI Bangalore  4 Lectures of 1.5 hrs each
  1.  The height of a polynomial, Mahler Measure and Mignotte’s Identity
  2.  Diophantine equation for polynomials
  3.   Waring’s problem for polynomials
  4.   Functional equations for polynomials
  5.   Representation of polynomials as sums of powers of linear functions
  6.   *Integer valued polynomials
S.K.Khanduja,IISER Mohali  4 Lectures of 1.5 hrs each
  1.  Main properties of irreducible polynomials
  2.  Eisenstein’s Criterion, Newton Polygons, Duma’s theorem and applications
  3.  Further Irreducibility criterion and applications
  4.  Irreducibility of trinomials and quadrinomials
  5.  Hilbert’s irreducibility theorem
  6.  *Integer valued polynomials
Chandrakant Aribam,IISER Mohali  4 Lectures of 1.5hrs each
  1.  The discriminant and the Galois group
  2.  Resolvent polynomials
  3.  The Galois group modulo p
  4.  Galois groups of Cubics and Quartics
  5.  Galois groups as permutation groups
  6.  Recognizing Galois groups Sn and An

References:

  1. Polynomials by Victor B.Prasolov

  2. Irreducibility Book by M.Filaseta (unpublished)

  3. Notesby K.Conrad

  4. Research papers

Time Table

 

Time

09:30–11:00

 

11:30 to 13:00

 

14:00 to 15:00

 

15:30 to 16:30

 
Mon
28Nov

SDA

 

SL

 

SDA/KH

 

SL/PY

 
Tue
29Nov

SDA

 

SL

L

SDA/KH

 

SL/PY

S
Wed
30Nov

SDA

T

CA

U

SDA/KH

 

CA/HS

N
Thu
1Dec

SDA

E

CA

N

SDA/KH

E

CA/HS

A
Fri
2Dec

CA

A

SL

C

CA/HS

A

SL/PY

C
Sat
3Dec

SK

 

CA

H

SK/MS

 

CA/HS

K
Sun
4Dec

 

 

 

 

 

 

 

 
Mon
5Dec

SK

 

SL

 

SK/MS

 

SL/PY

 
Tue
6Dec

SK

 

SL

L

SK/MS

 

SL/RB

S
Wed
7Dec

SK

T

BS

U

SL/MS

T

BS/SN

N
Thu
8Dec

BS

E

SL

N

BS/SN

E

SL/RB

A
Fri
9Dec

BS

A

SL

C

BS/SN

A

SL/RB

C
Sat
10Dec

BS

 

SL

H

BS/SN

 

SL/RB

K

Speakers:

  1. SDA=S.D.Adhikari

  2. SL=ShantaLaishram

  3. BS=B.Sury

  4. SK=S.K.Khanduja

  5. CA=ChandrakantAribam

Tutors:

  1. KH=Kh.Herachandra Singh

  2. RB=Ranjan Bera

  3. SN=Saranya Nair

  4. HS=H.Sharma

  5. MS=Mahinshi Singla

  6. PY=P.Yadav

 

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