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Goverment of India
DAE

Mathematics Ph.D Degree Programme

  • M.Sc. Programme
  • Ph.D Programme
  • Current Academic Timetable

Highlights of the Programme

Duration:

  • One year / Two years

Our Offering:

  • Students Completing 3 Years Of Undergraduate Studies Can Apply To Our 2 Years M.Sc. Programme (With An Exit Option At The End Of The First Year). This Programme Starts From 2025-2026 Academic Calendar.
  • Students Completing 4 Years Of Undergraduate Can Apply To Our 1 Year M.Sc. Programme. This Programme Will Start From 2026-2027 Academic Calendar.

How to Apply :

  • Apply to NBHM Scholarship Written Test (on 25/01/2025) (www.imsc.res.in/~nbhm/)
  • Shortlisted Students (According To The Cut-off Set By The HRI) Will Be Called For A Written Exam.

Students Entering In Year I Can

  • Exit After One Year With An M1 Diploma.
  • Exit After Two Years With A Two Year M.Sc. Degree.

Students Can Enter In Year II

  • Exit After One Year With An M2 Degree.
  • This Programme Will Start From 2026-2027 Academic Year.

Details Of The Curriculum

  • Course Curriculum Aims To Be More Research-oriented.
  • Well-blended Between Mandatory And Optional Courses.
  • Expected To Write A Master’s Thesis At The End, Under Faculty Supervision.
  • No Tuition/semsester Fee Will Be Charged From The Students.
  • Proposal For Scholarship Is Under Process.
  • The Degrees Will Be Granted By The Homi Bhabha National Institute.
  • There Are Provisions For The Students Who Excel In These Programs To Advance To Our Ph.D. Programme.

The Ph. D. Programme In Mathematics At Hri Consists Of A Rigorous Course Work And Projects In The First Two Semesters, Followed By Research Work Leading To A Ph.D. Degree. The Students Are Taught Basic As Well As Advanced Courses In Mathematics During This Period. They Also Get To Work On Projects In Which They Normally Continue To Work Towards Their Ph. D. Degree. A Thesis Supervisor Is Assigned To A Student Once He/she Passes The Oral General Comprehensive Examination (OGCE), Which Is Conducted After Successful Completions Of The Course Work.

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The Instructional Part Of The Doctoral Program Consists Of Pedagogical Lectures And Projects During The First Two Semesters. The Semesters Usually Start With The First Working Day Of August/january. Each Semester Is Of 16 Weeks Duration, Excluding Mid-semester Breaks And Examination Weeks. There Are Seven Core Courses And One Project Of Total 60 Credits In The First Year Of The Programme.

Syllabus & Credit Details:

Semester ICreditsSemester IICredits
Algebra I4Algebra II4
Analysis I4Analysis II4
Topology I4Topology II4
Differentiable Manifolds4Project2
Research Methodology9  

(*The Topics Covered In A Certain Course May Vary Depending On The Instructor.)

Credits: Each Credit Stands For 25 To 30 Hours Of Workload, Where The Workload Includes The Time Students Typically Need To Complete All Learning Activities Such As Attending Lectures, Completing Assignments, Self Study, Preparing For Seminars Etc.

In Research Methodology, Students Are Expected To Get Familiarised With The Process Of Writing Academic Reports, Planning Of A Research Project, Writing Mathematical Texts Using Latex Software And Oral Presentation. The Students Are Also Expected To Be Familiarised With Research And Publication Ethics.

Project Consists Of A Semester-long Reading Courses Under The Supervision Of A Faculty, And Evaluated Based On A Typewritten Report (Using The Latex Software), Of The Study Carried Out By The Student And A Seminar Given At The End Of The Semester.

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  • Evaluation Of All Instruction Based Courses Shall Follow The Usual Pattern, That Is, Through Mid-semester, Final-semester Examinations And Assignments/internal Assessment. Answer Sheets Of Mid Term And Final Examinations Will Be Shown To The Students By The Instructors.
  • If A Student Fails In A Course, The Re-examination For That Course Will Be Conducted During The Break Between The First And The Second Years. The Examiner May Opt To Give An Assignment In The Re-examination, But The Weightage For The Assignment Should Not Be More Than 20%.
  • If A Student Fails In The Re-examination, Then The Mathematics Graduate Studies Committee (Mgsc) Will Make One Of The Following Recommendations To The Director: (I) The Student Does Not Have The Capacity To Pursue The Programme; (Ii) The Student May Be Given One More Chance After Repeating The Failed Courses. If Option (Ii) Is Chosen, Then The Mgsc Will Assign Instructors For These Courses In The Third Semester Itself. These Could Be Reading Courses.
  • Ogce: The Ogce Will Be Held Within Three Months After Completion Of The Second Semester Course Work For The Students Passed In All Courses. A Student Is Declared Passed If He/she Secures Minimum 50% Marks In All Individual Courses And 60% Aggregate. This Is An Hbni (Homi-bhaba National Institute) Requirement For Continuing The Ph.d. Programme At Hri.
  • For The Course Work Starting In The Month Of August, The Second Semester Courses Will Be Completed By 15th May Of The Coming Year, And Therefore The Ogce Will Be Conducted By 15th August. The Exact Date Of Ogce Will Be Communicated To The Students By The Mgsc Towards The End Of The Second Semester. The Ogce For The Students Who Are Re-doing Some Courses Should Be Conducted Latest By Middle Of The Second Academic Year.
  • The Ogce Is To Ensure That The Student Has Gained A Solid Foundation In Basic Mathematics, As Expected From The Course Work. The Student Will Be Examined Accordingly, Based On All The Subjects Taught In The First Year Course Work At Hri. However, The Students May Be Given An Option To Prioritise On Two Out Of Three Main Areas For Ogce, Namely Algebra, Analysis And Topology.
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Algebra and Algebraic Geometry

Group Theory (Manoj Kumar Yadav)

Abstract Group Theory: Automorphisms, Conjugacy Classes, Commutator Word Map, And Low Dimensional Cohomology; Braces And Skew Braces; Yang-baxter Equation.

Representation Theory (Punita Batra)

Representations of Lie Algebras: Semisimple, Toroidal Lie Algebras.

Algebraic Geometry (Umesh Dubey, B.S.S. Sreedhar)

Derived Categories Of Coherent Sheaves, Matrix Factorization Categories, Tensor Triangulated Categories And T-structures, Algebraic Stacks, Algebraic K-theory, And Chow Groups.

*Some Familiar Topics in Algebra & Algebraic Geometry to Carry Out `Research Projects’ , See here.

Number Theory

Analytic Number Theory (D Surya Ramana, Gyan Prakash, R Thangadurai)

Ramsey Theory And Additive Representation Problems In Analytic Number Theory, Additive Combinatorics, Transcendental Number Theory.

Arithmetic Geometry (Aprameyo Pal, Jishnu Ray)

Iwasawa Theory, Special Values Of L-functions, Automorphic Representations And P-adic Families, Galois Representations, P-adic Hodge Theory And Langlands Program, Mod-p Modular Arithmetic, Drinfeld Modules.

*Some Familiar Topics in Number Theory to carry out `Research Projects’ , See here.

Analysis

Partial Differential Equations (Tuhin Ghosh, Amrita Ghosh)

Analysis Of Partial Differential Equations, Inverse Problems, Homogenization, Mathematical Fluid Dynamics.

Harmonic Analysis (P K Ratnakumar)

Harmonic Analysis Of Hermite, Special Hermite, And Laguerre Differential Operators.

*Some Familiar Topics in Analysis to Carry Out `Research Projects’ , See here.

Geometry

Differential Geometry (Hemangi M. Shah)

Riemannian Geometry, Finsler Geometry.

*Some Familiar Topics in Geometry to Carry Out `Research Projects’ , See here.

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Doctoral Committee: After the Successful Completion of the First Year Course Work and the OGCE, the MGSC Will Assign a Thesis Supervisor to a Student, Taking Consent From the Faculty Member, and Constitute a Doctoral Committee to Monitor the Academic Progress of the Student. The Doctoral Committee Consists of a Chairman (a Faculty Member at the Level of Professor/ Associate Professor), the Supervisor as the Convenor, and Three Members (Faculty), Who Could Also Be Experts From Outside HRI.

Annual Progress Report: Every Student is Required to Submit a Progress Report at the End of the Academic Year, and Deliver a Fellowship Extension Seminar in Front of the Doctoral Committee. The Thesis Supervisor Will Call a Doctoral Committee Meeting Two Months Before the End of Every Academic Year, and Arrange a Seminar by the Student Based on the Work Done in the Current Academic Year. The Thesis Supervisor Will Discuss the Progress Report Submitted by the Student With the Members of the Doctoral Committee, and Prepare a Progress Report in Consultation With Them. The Doctoral Committee Will Also Give Guidelines for Future Research.

Fellowship Extension: The Fellowship Extension Will Be Based on the Recommendation by the Doctoral Committee and the Approval From HBNI (Homi-Bhaba National Institute), the Deemed University Where All Students of HRI Are Registered for Their Ph.D. Degree: http:// www.hbni.ac.in/ . Thus the Students Are Required to Upload the Annual Progress Report Signed by the Doctoral Committee Members and the Dean Academic, to the Anuvidya website http:// www.anuvidhya.in , Preferably Within Two Weeks After the Extension Seminar. The Original Annual Progress Report Should Be Submitted to the HBNI Cell at HRI, for Records.

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Once the Thesis Supervisor Feels That There is Enough Work That Qualifies for a Ph.D. Degree, the Student Can Start Preparing the Thesis, as Per the Advise of the Supervisor.

A Synopsis Talk Needs to Be Arranged Before the Synopsis Submission. The Thesis Has to Be Submitted, Within Three Months After the Submission of the Synopsis.

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Graduate Courseworks - Timeline (2024-2025)

Semester II

First day of instruction: 6 January 2025
Mid-semester exam: 3 March – 7 March 2025
Last day of instruction: 8 May 2025
End Sem Exam: 14 May – 20 May 2025
Deadline to submit the marks: 27 May 2025

Semester I

First day of instruction: 5 August, 2024
Mid-semester exam week: 30 September – 4 October, 2024
Last day of instruction: 29 November, 2024
End-semester exam week: 2 – 6 December, 2024
Deadline for submission of grades: 13 December, 2024

Independence Term 2024

(August 5, 2024–November 29, 2024)

M.Sc. First Year

Lectures will be held in the String Area Lecture Hall.

9:30–10:55 11:05–12:30 13:30–14:55 15:05–16:30
MONDAY QM-1 ED CM
TUESDAY QM-1 MM-1 Lab Lab
WEDNESDAY MM-1 Lab Lab
THURSDAY QM-1 CM ED MM-1
FRIDAY ED CM
Course Instructor
Classical Mechanics (CM) S. Dasgupta
Electrodynamics (ED) T. Ghosh
Laboratory (Lab) S. L. Gupta
Mathematical Methods 1 (MM-1) Tapas Das
Quantum Mechanics 1 (QM-1) D. Jatkar
 

M.Sc. Second Year and Ph.D.

Lectures will be held in the Higgs Lecture Hall.

9:30–10:55 11:05–12:30 13:30–14:55 15:05–16:30
MONDAY QIC-1 QM-3 MM-2 CMP
TUESDAY QFT-1 QM-3 GR/MOE MM-2
WEDNESDAY QIC-1/GR CMP MOE QFT-1
THURSDAY CMP QIC-1 MM-2 QM-3
FRIDAY GR QFT-1 MOE

GR lectures will be held in the String Area Lecture Hall.

Course Instructor
Condensed Matter Physics (CMP) Tisita Das
General Relativity (GR) D. P. Jatkar
Mathematical Methods 2 (MM-2) U. Sen
Matter Out of Equilibrium (MOE) P. Majumdar
Quantum Field Theory 1 (QFT-1) S. K. Rai
Quantum Info. and Computation 1 (QIC-1) A. Sen De
Quantum Mechanics 3 (QM-3) S. Chakraborty

Please contact instructors of reading courses to fix the schedule.

Mid-Term Week: September 30 – October 4, 2024
End-term week: November 25-29, 2024
Mid-term break: October 7-11, 2024

The Ph.D. program in mathematics is open to students having a Master’s degree in mathematics. The program consists of a rigorous course work and projects during the first three semesters, followed by research work leading to a Ph.D. degree. The Degree is granted by the Homi Bhabha National Institute (HBNI).

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Last Updated on : December 2, 2024