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Faculty Dr Sazzad Ali Biswas
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Dr Sazzad Ali Biswas

Assistant Professor

Department of Mathematics

Contact Details

sazzadali.b@srmap.edu.in

Office Location

School of Engineering and Sciences Mathematics Faculty Dr Sazzad Ali Biswas

Faculty Information

Education

2016
PhD
University of Hyderabad
India
2008
MSc
Jadavpur University
India
2006
BSc
Jadavpur University
India

Personal Website

Experience

  • ACADEMIC POSITIONS
  • Visiting Researcher, University of Copenhagen, Denmark, December 01, 2020 to March 31, 2021.
  • Postdoctoral Fellow, University of Copenhagen, Denmark, October 1, 2019 to November 30, 2020.
  • Postdoctoral Fellow, Hebrew University of Jerusalem, Israel, July 15, 2018 to September 30, 2019.
  • Visiting Faculty, Chennai Mathematical Institute, Chennai, India, December 06, 2015 - July 12, 2018.
  • Visiting Scientist, Weizmann Institute of Science, Israel, May - June, 2017.
  • Visiting Fellow, Ecole Normale Suprieure de Lyon and University of Lyon 1, Lyon, France, April 21 - June 30, 2018.
  • Visiting scholar, Humboldt University, Berlin, Germany, September 2011 - May 2012.
  • SHORT-TERM ACADEMIC VISIT
  • University of Duisburg-Essen, Germany, June 16-30, 2019.
  • MSRI, Berkely, USA, April 08-12, 2019.
  • Tata Institute of Fundamental Reseach, Mumbai, September 11-14, 2015.
  • Harish-Chandra Reseach Institute, Allahabad, Nov 1-30, 2015.
  • TEACHING EXPERIENCES (AS AN INSTRUCTOR)
  • August - November, 2016, p-adic Analysis, Chennai Mathematical Institute (CMI), Chennai, India.
  • August - November, 2017, Arithmetic Geometry, CMI.
  • January - April, 2018, Algebraic Number Theory, CMI.

Research Interest

  • Converse Problem in the Galois side: In the automorphic side of Langlands program, there are converse theorems. But in the Galois side, we do not have any such theorems. Currently, I have been trying to give a converse theorem for local Galois representations.
  • Geometric Analog of epsilon factors: By work of Robert Langlands and P. Deligne we can attach a unique complex number (which we call epsilon factor) for a given complex Galois representation. We also can attach a similar constant for a given elliptic curve over number field. But the relationship between epsilon factors of Galois representations and elliptic curves are not yet known. An explicit connection between these epsilon factors are very much important in arithmetic geometry. I am trying to find a result which connect them.
  • Galois representations and Analytic torsion: I also have been trying to construct Galois representations by using analytic torsions for some Riemannian manifolds.

Awards

  • Postdoctoral Fellowship from the University of Copenhagen, Denmark, 2019.
  • Postdoctoral Fellowship from the Israel Science Foundation (grant no: 1676/17) at the Hebrew University of Jerusalem, Israel, 2018.
  • Postdoctoral Fellowship from the Chennai Mathematical Institute and the Infosys Foundation, India, 2015.
  • IMU-Berlin Einstein Foundation Fellowship for nine months in Berlin, Germany, 2011.
  • Received National Scholarship for the period: 2001-2006, Govt. of India.
  • Qualified in NET Examination held in December, 2007 and June, 2008 with CSIR Fellowship, Govt. of India.
  • Qualified in GATE, 2008, Govt. of India.
  • Postdoctoral Fellowship at Harish-Chandra Research Institute, Allahabad, India, 2016 (did not avail).
  • Postdoctoral Fellowship at Indian Statistical Institute, Bangalore, India, 2016 (did not avail).
  • International travel grant from DST and NBHM for attending workshop and conference in Italy, 2011.
  • Travel grant from the Ecole Normale Suprieure de Lyon, France, 2018.
  • 700 USD nancial support from the MSRI, Berkeley, USA, 2019.
  • Travel grant from the University of Duisburg-Essen, Germany, 2019.
  • Travel support from the Berlin Mathematical School, Berlin, Germany, 2011.

Memberships

Publications

  • Local root numbers for heisenberg-representations – Some explicit results

    Biswas S.A., Zink E.-W.

    Article, International Journal of Mathematics, 2021, DOI Link

    View abstract ⏷

    Heisenberg representations ρ of (pro-)finite groups G are by definition irreducible representations of the two-step nilpotent factor group G/C3G. Better known are Heisenberg groups which can be understood as allowing faithful Heisenberg representations. A special feature is that ρ = IndHG(χ H) will be induced by characters (H,χH) of subgroups in multiple ways, where the pairs (H,χH) can be interpreted as maximal isotropic pairs. If F|ℚp is a p-adic number field and G = GF the absolute Galois group then maximal isotropic pairs rewrite as (E,χE), where E|F is an abelian extension and χE:E×→ ℂ× a character. We will consider the extended local Artin-root-number W(ρ,ψ) for those ρ which are essentially tame and express it by a formula not depending on the various maximal isotropic pairs (E,χE) for ρ.

  • Epsilon factors of symplectic type characters in the wild case

    Biswas S.A.

    Article, Forum Mathematicum, 2021, DOI Link

    View abstract ⏷

    By work of John Tate we can associate an epsilon factor with every multiplicative character of a local field. In this paper, we determine the explicit signs of the epsilon factors for symplectic type characters of K×, where K/F is a wildly ramified quadratic extension of a non-Archimedean local field F of characteristic zero.

  • Langlands lambda function for quadratic tamely ramified extensions

    Biswas S.A.

    Article, Journal of Algebra and its Applications, 2019, DOI Link

    View abstract ⏷

    Let K/F be a quadratic tamely ramified extension of a non-Archimedean local field F of characteristic zero. In this paper, we give an explicit formula for Langlands' lambda function λK/F.

  • Computation of the Lambda function for a finite Galois extension

    Biswas S.A.

    Article, Journal of Number Theory, 2018, DOI Link

    View abstract ⏷

    By Langlands [13], and Deligne [4] we know that the local constants are extendible functions. Therefore, to give an explicit formula of the local constant of an induced representation of a local Galois group of a non-Archimedean local field F of characteristic zero, we have to compute the lambda function λK/F for a finite extension K/F. In this paper, when a finite extension K/F is Galois, we give a formula for λK/F.

  • Invariant formula of the determinant of a Heisenberg representation

    Biswas S.A.

    Article, International Journal of Mathematics, 2017, DOI Link

    View abstract ⏷

    In this paper, we give an explicit formula of the determinant of a Heisenberg representation ρ of a finite group G. Heisenberg representations are induced by 1-dimensional characters in multiple ways, but our formula will be independent of any particular choice of induction.

  • Twisting formula of epsilon factors

    Biswas S.A.

    Article, Proceedings of the Indian Academy of Sciences: Mathematical Sciences, 2017, DOI Link

    View abstract ⏷

    For characters of a non-Archimedean local field we have explicit formula for epsilon factors. But in general, we do not have any generalized twisting formula of epsilon factors. In this paper, we give a generalized twisting formula of epsilon factors via local Jacobi sums.

Patents

Projects

Scholars

Doctoral Scholars

  • Pate Swati Baliram

Interests

  • Arithmetic geometry
  • Automorphic and Galois representations
  • Cryptography
  • Langlands Program

Thought Leaderships

There are no Thought Leaderships associated with this faculty.

Top Achievements

Education
2006
BSc
Jadavpur University
India
2008
MSc
Jadavpur University
India
2016
PhD
University of Hyderabad
India
Experience
  • ACADEMIC POSITIONS
  • Visiting Researcher, University of Copenhagen, Denmark, December 01, 2020 to March 31, 2021.
  • Postdoctoral Fellow, University of Copenhagen, Denmark, October 1, 2019 to November 30, 2020.
  • Postdoctoral Fellow, Hebrew University of Jerusalem, Israel, July 15, 2018 to September 30, 2019.
  • Visiting Faculty, Chennai Mathematical Institute, Chennai, India, December 06, 2015 - July 12, 2018.
  • Visiting Scientist, Weizmann Institute of Science, Israel, May - June, 2017.
  • Visiting Fellow, Ecole Normale Suprieure de Lyon and University of Lyon 1, Lyon, France, April 21 - June 30, 2018.
  • Visiting scholar, Humboldt University, Berlin, Germany, September 2011 - May 2012.
  • SHORT-TERM ACADEMIC VISIT
  • University of Duisburg-Essen, Germany, June 16-30, 2019.
  • MSRI, Berkely, USA, April 08-12, 2019.
  • Tata Institute of Fundamental Reseach, Mumbai, September 11-14, 2015.
  • Harish-Chandra Reseach Institute, Allahabad, Nov 1-30, 2015.
  • TEACHING EXPERIENCES (AS AN INSTRUCTOR)
  • August - November, 2016, p-adic Analysis, Chennai Mathematical Institute (CMI), Chennai, India.
  • August - November, 2017, Arithmetic Geometry, CMI.
  • January - April, 2018, Algebraic Number Theory, CMI.
Research Interests
  • Converse Problem in the Galois side: In the automorphic side of Langlands program, there are converse theorems. But in the Galois side, we do not have any such theorems. Currently, I have been trying to give a converse theorem for local Galois representations.
  • Geometric Analog of epsilon factors: By work of Robert Langlands and P. Deligne we can attach a unique complex number (which we call epsilon factor) for a given complex Galois representation. We also can attach a similar constant for a given elliptic curve over number field. But the relationship between epsilon factors of Galois representations and elliptic curves are not yet known. An explicit connection between these epsilon factors are very much important in arithmetic geometry. I am trying to find a result which connect them.
  • Galois representations and Analytic torsion: I also have been trying to construct Galois representations by using analytic torsions for some Riemannian manifolds.
Awards & Fellowships
  • Postdoctoral Fellowship from the University of Copenhagen, Denmark, 2019.
  • Postdoctoral Fellowship from the Israel Science Foundation (grant no: 1676/17) at the Hebrew University of Jerusalem, Israel, 2018.
  • Postdoctoral Fellowship from the Chennai Mathematical Institute and the Infosys Foundation, India, 2015.
  • IMU-Berlin Einstein Foundation Fellowship for nine months in Berlin, Germany, 2011.
  • Received National Scholarship for the period: 2001-2006, Govt. of India.
  • Qualified in NET Examination held in December, 2007 and June, 2008 with CSIR Fellowship, Govt. of India.
  • Qualified in GATE, 2008, Govt. of India.
  • Postdoctoral Fellowship at Harish-Chandra Research Institute, Allahabad, India, 2016 (did not avail).
  • Postdoctoral Fellowship at Indian Statistical Institute, Bangalore, India, 2016 (did not avail).
  • International travel grant from DST and NBHM for attending workshop and conference in Italy, 2011.
  • Travel grant from the Ecole Normale Suprieure de Lyon, France, 2018.
  • 700 USD nancial support from the MSRI, Berkeley, USA, 2019.
  • Travel grant from the University of Duisburg-Essen, Germany, 2019.
  • Travel support from the Berlin Mathematical School, Berlin, Germany, 2011.
Memberships
Publications

  • Local root numbers for heisenberg-representations – Some explicit results

    Biswas S.A., Zink E.-W.

    Article, International Journal of Mathematics, 2021, DOI Link

    View abstract ⏷

    Heisenberg representations ρ of (pro-)finite groups G are by definition irreducible representations of the two-step nilpotent factor group G/C3G. Better known are Heisenberg groups which can be understood as allowing faithful Heisenberg representations. A special feature is that ρ = IndHG(χ H) will be induced by characters (H,χH) of subgroups in multiple ways, where the pairs (H,χH) can be interpreted as maximal isotropic pairs. If F|ℚp is a p-adic number field and G = GF the absolute Galois group then maximal isotropic pairs rewrite as (E,χE), where E|F is an abelian extension and χE:E×→ ℂ× a character. We will consider the extended local Artin-root-number W(ρ,ψ) for those ρ which are essentially tame and express it by a formula not depending on the various maximal isotropic pairs (E,χE) for ρ.

  • Epsilon factors of symplectic type characters in the wild case

    Biswas S.A.

    Article, Forum Mathematicum, 2021, DOI Link

    View abstract ⏷

    By work of John Tate we can associate an epsilon factor with every multiplicative character of a local field. In this paper, we determine the explicit signs of the epsilon factors for symplectic type characters of K×, where K/F is a wildly ramified quadratic extension of a non-Archimedean local field F of characteristic zero.

  • Langlands lambda function for quadratic tamely ramified extensions

    Biswas S.A.

    Article, Journal of Algebra and its Applications, 2019, DOI Link

    View abstract ⏷

    Let K/F be a quadratic tamely ramified extension of a non-Archimedean local field F of characteristic zero. In this paper, we give an explicit formula for Langlands' lambda function λK/F.

  • Computation of the Lambda function for a finite Galois extension

    Biswas S.A.

    Article, Journal of Number Theory, 2018, DOI Link

    View abstract ⏷

    By Langlands [13], and Deligne [4] we know that the local constants are extendible functions. Therefore, to give an explicit formula of the local constant of an induced representation of a local Galois group of a non-Archimedean local field F of characteristic zero, we have to compute the lambda function λK/F for a finite extension K/F. In this paper, when a finite extension K/F is Galois, we give a formula for λK/F.

  • Invariant formula of the determinant of a Heisenberg representation

    Biswas S.A.

    Article, International Journal of Mathematics, 2017, DOI Link

    View abstract ⏷

    In this paper, we give an explicit formula of the determinant of a Heisenberg representation ρ of a finite group G. Heisenberg representations are induced by 1-dimensional characters in multiple ways, but our formula will be independent of any particular choice of induction.

  • Twisting formula of epsilon factors

    Biswas S.A.

    Article, Proceedings of the Indian Academy of Sciences: Mathematical Sciences, 2017, DOI Link

    View abstract ⏷

    For characters of a non-Archimedean local field we have explicit formula for epsilon factors. But in general, we do not have any generalized twisting formula of epsilon factors. In this paper, we give a generalized twisting formula of epsilon factors via local Jacobi sums.
Contact Details

sazzadali.b@srmap.edu.in

Scholars

Doctoral Scholars

  • Pate Swati Baliram

Interests

  • Arithmetic geometry
  • Automorphic and Galois representations
  • Cryptography
  • Langlands Program

Education
2006
BSc
Jadavpur University
India
2008
MSc
Jadavpur University
India
2016
PhD
University of Hyderabad
India
Experience
  • ACADEMIC POSITIONS
  • Visiting Researcher, University of Copenhagen, Denmark, December 01, 2020 to March 31, 2021.
  • Postdoctoral Fellow, University of Copenhagen, Denmark, October 1, 2019 to November 30, 2020.
  • Postdoctoral Fellow, Hebrew University of Jerusalem, Israel, July 15, 2018 to September 30, 2019.
  • Visiting Faculty, Chennai Mathematical Institute, Chennai, India, December 06, 2015 - July 12, 2018.
  • Visiting Scientist, Weizmann Institute of Science, Israel, May - June, 2017.
  • Visiting Fellow, Ecole Normale Suprieure de Lyon and University of Lyon 1, Lyon, France, April 21 - June 30, 2018.
  • Visiting scholar, Humboldt University, Berlin, Germany, September 2011 - May 2012.
  • SHORT-TERM ACADEMIC VISIT
  • University of Duisburg-Essen, Germany, June 16-30, 2019.
  • MSRI, Berkely, USA, April 08-12, 2019.
  • Tata Institute of Fundamental Reseach, Mumbai, September 11-14, 2015.
  • Harish-Chandra Reseach Institute, Allahabad, Nov 1-30, 2015.
  • TEACHING EXPERIENCES (AS AN INSTRUCTOR)
  • August - November, 2016, p-adic Analysis, Chennai Mathematical Institute (CMI), Chennai, India.
  • August - November, 2017, Arithmetic Geometry, CMI.
  • January - April, 2018, Algebraic Number Theory, CMI.
Research Interests
  • Converse Problem in the Galois side: In the automorphic side of Langlands program, there are converse theorems. But in the Galois side, we do not have any such theorems. Currently, I have been trying to give a converse theorem for local Galois representations.
  • Geometric Analog of epsilon factors: By work of Robert Langlands and P. Deligne we can attach a unique complex number (which we call epsilon factor) for a given complex Galois representation. We also can attach a similar constant for a given elliptic curve over number field. But the relationship between epsilon factors of Galois representations and elliptic curves are not yet known. An explicit connection between these epsilon factors are very much important in arithmetic geometry. I am trying to find a result which connect them.
  • Galois representations and Analytic torsion: I also have been trying to construct Galois representations by using analytic torsions for some Riemannian manifolds.
Awards & Fellowships
  • Postdoctoral Fellowship from the University of Copenhagen, Denmark, 2019.
  • Postdoctoral Fellowship from the Israel Science Foundation (grant no: 1676/17) at the Hebrew University of Jerusalem, Israel, 2018.
  • Postdoctoral Fellowship from the Chennai Mathematical Institute and the Infosys Foundation, India, 2015.
  • IMU-Berlin Einstein Foundation Fellowship for nine months in Berlin, Germany, 2011.
  • Received National Scholarship for the period: 2001-2006, Govt. of India.
  • Qualified in NET Examination held in December, 2007 and June, 2008 with CSIR Fellowship, Govt. of India.
  • Qualified in GATE, 2008, Govt. of India.
  • Postdoctoral Fellowship at Harish-Chandra Research Institute, Allahabad, India, 2016 (did not avail).
  • Postdoctoral Fellowship at Indian Statistical Institute, Bangalore, India, 2016 (did not avail).
  • International travel grant from DST and NBHM for attending workshop and conference in Italy, 2011.
  • Travel grant from the Ecole Normale Suprieure de Lyon, France, 2018.
  • 700 USD nancial support from the MSRI, Berkeley, USA, 2019.
  • Travel grant from the University of Duisburg-Essen, Germany, 2019.
  • Travel support from the Berlin Mathematical School, Berlin, Germany, 2011.
Memberships
Publications

  • Local root numbers for heisenberg-representations – Some explicit results

    Biswas S.A., Zink E.-W.

    Article, International Journal of Mathematics, 2021, DOI Link

    View abstract ⏷

    Heisenberg representations ρ of (pro-)finite groups G are by definition irreducible representations of the two-step nilpotent factor group G/C3G. Better known are Heisenberg groups which can be understood as allowing faithful Heisenberg representations. A special feature is that ρ = IndHG(χ H) will be induced by characters (H,χH) of subgroups in multiple ways, where the pairs (H,χH) can be interpreted as maximal isotropic pairs. If F|ℚp is a p-adic number field and G = GF the absolute Galois group then maximal isotropic pairs rewrite as (E,χE), where E|F is an abelian extension and χE:E×→ ℂ× a character. We will consider the extended local Artin-root-number W(ρ,ψ) for those ρ which are essentially tame and express it by a formula not depending on the various maximal isotropic pairs (E,χE) for ρ.

  • Epsilon factors of symplectic type characters in the wild case

    Biswas S.A.

    Article, Forum Mathematicum, 2021, DOI Link

    View abstract ⏷

    By work of John Tate we can associate an epsilon factor with every multiplicative character of a local field. In this paper, we determine the explicit signs of the epsilon factors for symplectic type characters of K×, where K/F is a wildly ramified quadratic extension of a non-Archimedean local field F of characteristic zero.

  • Langlands lambda function for quadratic tamely ramified extensions

    Biswas S.A.

    Article, Journal of Algebra and its Applications, 2019, DOI Link

    View abstract ⏷

    Let K/F be a quadratic tamely ramified extension of a non-Archimedean local field F of characteristic zero. In this paper, we give an explicit formula for Langlands' lambda function λK/F.

  • Computation of the Lambda function for a finite Galois extension

    Biswas S.A.

    Article, Journal of Number Theory, 2018, DOI Link

    View abstract ⏷

    By Langlands [13], and Deligne [4] we know that the local constants are extendible functions. Therefore, to give an explicit formula of the local constant of an induced representation of a local Galois group of a non-Archimedean local field F of characteristic zero, we have to compute the lambda function λK/F for a finite extension K/F. In this paper, when a finite extension K/F is Galois, we give a formula for λK/F.

  • Invariant formula of the determinant of a Heisenberg representation

    Biswas S.A.

    Article, International Journal of Mathematics, 2017, DOI Link

    View abstract ⏷

    In this paper, we give an explicit formula of the determinant of a Heisenberg representation ρ of a finite group G. Heisenberg representations are induced by 1-dimensional characters in multiple ways, but our formula will be independent of any particular choice of induction.

  • Twisting formula of epsilon factors

    Biswas S.A.

    Article, Proceedings of the Indian Academy of Sciences: Mathematical Sciences, 2017, DOI Link

    View abstract ⏷

    For characters of a non-Archimedean local field we have explicit formula for epsilon factors. But in general, we do not have any generalized twisting formula of epsilon factors. In this paper, we give a generalized twisting formula of epsilon factors via local Jacobi sums.
Contact Details

sazzadali.b@srmap.edu.in

Scholars

Doctoral Scholars

  • Pate Swati Baliram