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1:54:58 Institut des Hautes Études Scientifiques (IHÉS) English 2013

3/4 Mathematical Structures arising from Genetics and Molecular Biology

  • Published: 2013
  • Publisher: Institut des Hautes Études Scientifiques (IHÉS)
  • Language: English
1:59:46 Institut des Hautes Études Scientifiques (IHÉS) English 2013

4/4 Mathematical Structures arising from Genetics and Molecular Biology

  • Published: 2013
  • Publisher: Institut des Hautes Études Scientifiques (IHÉS)
  • Language: English
1:21:11 Institut des Hautes Études Scientifiques (IHÉS) English 2014

3/6 Nilsequences

Classical Fourier analysis has found many uses in additive number theory. However, while it is well-adapted to some pro - blems, it is unable to handle others. For example, if one has a set A, and one wishes to know how many 3-term arithmetic progressions are contained in A, then Fourier analysis is useful, but if one wishes to count 4-term progressions then it is not. For this, and other, problems the more general notion of a nilsequence is required. NIlsequences are a kind of «higher order character» forming the basis of what is becoming known as «higher-order Fourier analysis». The talks will be about this theory.
  • Published: 2014
  • Publisher: Institut des Hautes Études Scientifiques (IHÉS)
  • Language: English
1:23:21 Institut des Hautes Études Scientifiques (IHÉS) English 2014

4/4 Spectral Geometric Unification

Order one condition and physics beyond Standard Model.
  • Published: 2014
  • Publisher: Institut des Hautes Études Scientifiques (IHÉS)
  • Language: English
1:29:19 Institut des Hautes Études Scientifiques (IHÉS) English 2014

4/6 Nilsequences

Classical Fourier analysis has found many uses in additive number theory. However, while it is well-adapted to some pro - blems, it is unable to handle others. For example, if one has a set A, and one wishes to know how many 3-term arithmetic progressions are contained in A, then Fourier analysis is useful, but if one wishes to count 4-term progressions then it is not. For this, and other, problems the more general notion of a nilsequence is required. NIlsequences are a kind of «higher order character» forming the basis of what is becoming known as «higher-order Fourier analysis». The talks will be about this theory.
  • Published: 2014
  • Publisher: Institut des Hautes Études Scientifiques (IHÉS)
  • Language: English
1:51:28 Institut des Hautes Études Scientifiques (IHÉS) English 2013

2/4 Mathematical Structures arising from Genetics and Molecular Biology

  • Published: 2013
  • Publisher: Institut des Hautes Études Scientifiques (IHÉS)
  • Language: English
2:04:24 Institut des Hautes Études Scientifiques (IHÉS) English 2014

4/4 Universal mixed elliptic motives

Universal mixed elliptic motives are certain local systems over a modular curve that are endowed with additional structure, such as that of a variation of mixed Hodge structure. They form a tannakian category. The coordinate ring of its fundamental group is a Hopf algebra in a category of mixed Tate motives. This course will be an introduction to universal mixed elliptic motives, which were defined with Makoto Matsumoto, and a report on more recent developments. One focus will be on the structure of the tannakian fundamental group of the category of mixed elliptic motives over M1,1. In particular, we will explain that it is an extension of GL2 by a prounipotent group whose Lie algebra is generated by Eisenstein series and has non-trivial relations coming from cusp forms. We will also discuss the relation of mixed elliptic motives to mixed Tate motives via specialization to the Tate curve and the nodal cubic.
  • Published: 2014
  • Publisher: Institut des Hautes Études Scientifiques (IHÉS)
  • Language: English
1:43:44 Institut des Hautes Études Scientifiques (IHÉS) English 2013

1/4 Mathematical Structures arising from Genetics and Molecular Biology

  • Published: 2013
  • Publisher: Institut des Hautes Études Scientifiques (IHÉS)
  • Language: English
2:07:21 Institut des Hautes Études Scientifiques (IHÉS) English 2014

2/4 Universal mixed elliptic motives

Universal mixed elliptic motives are certain local systems over a modular curve that are endowed with additional structure, such as that of a variation of mixed Hodge structure. They form a tannakian category. The coordinate ring of its fundamental group is a Hopf algebra in a category of mixed Tate motives. This course will be an introduction to universal mixed elliptic motives, which were defined with Makoto Matsumoto, and a report on more recent developments. One focus will be on the structure of the tannakian fundamental group of the category of mixed elliptic motives over M1,1. In particular, we will explain that it is an extension of GL2 by a prounipotent group whose Lie algebra is generated by Eisenstein series and has non-trivial relations coming from cusp forms. We will also discuss the relation of mixed elliptic motives to mixed Tate motives via specialization to the Tate curve and the nodal cubic.
  • Published: 2014
  • Publisher: Institut des Hautes Études Scientifiques (IHÉS)
  • Language: English
1:34:15 Institut des Hautes Études Scientifiques (IHÉS) English 2014

3/4 Spectral Geometric Unification

Spectral action and Standard Model of Particle Physics.
  • Published: 2014
  • Publisher: Institut des Hautes Études Scientifiques (IHÉS)
  • Language: English
1:50:23 Institut des Hautes Études Scientifiques (IHÉS) English 2014

1/4 Universal mixed elliptic motives

Universal mixed elliptic motives are certain local systems over a modular curve that are endowed with additional structure, such as that of a variation of mixed Hodge structure. They form a tannakian category. The coordinate ring of its fundamental group is a Hopf algebra in a category of mixed Tate motives. This course will be an introduction to universal mixed elliptic motives, which were defined with Makoto Matsumoto, and a report on more recent developments. One focus will be on the structure of the tannakian fundamental group of the category of mixed elliptic motives over M1,1. In particular, we will explain that it is an extension of GL2 by a prounipotent group whose Lie algebra is generated by Eisenstein series and has non-trivial relations coming from cusp forms. We will also discuss the relation of mixed elliptic motives to mixed Tate motives via specialization to the Tate curve and the nodal cubic.
  • Published: 2014
  • Publisher: Institut des Hautes Études Scientifiques (IHÉS)
  • Language: English
1:24:23 Institut des Hautes Études Scientifiques (IHÉS) English 2014

2/4 Spectral Geometric Unification

Classification of finite spaces and basis for geometric unification.
  • Published: 2014
  • Publisher: Institut des Hautes Études Scientifiques (IHÉS)
  • Language: English
1:25:30 Institut des Hautes Études Scientifiques (IHÉS) English 2014

5/6 Nilsequences

Classical Fourier analysis has found many uses in additive number theory. However, while it is well-adapted to some pro - blems, it is unable to handle others. For example, if one has a set A, and one wishes to know how many 3-term arithmetic progressions are contained in A, then Fourier analysis is useful, but if one wishes to count 4-term progressions then it is not. For this, and other, problems the more general notion of a nilsequence is required. NIlsequences are a kind of «higher order character» forming the basis of what is becoming known as «higher-order Fourier analysis». The talks will be about this theory.
  • Published: 2014
  • Publisher: Institut des Hautes Études Scientifiques (IHÉS)
  • Language: English
1:31:46 Institut des Hautes Études Scientifiques (IHÉS) English 2014

1/4 Spectral Geometric Unification

A brief introduction to noncommutative geometry with emphasis on the essential tools used in physics.
  • Published: 2014
  • Publisher: Institut des Hautes Études Scientifiques (IHÉS)
  • Language: English
1:52:46 Institut des Hautes Études Scientifiques (IHÉS) English 2014

3/4 Universal mixed elliptic motives

Universal mixed elliptic motives are certain local systems over a modular curve that are endowed with additional structure, such as that of a variation of mixed Hodge structure. They form a tannakian category. The coordinate ring of its fundamental group is a Hopf algebra in a category of mixed Tate motives. This course will be an introduction to universal mixed elliptic motives, which were defined with Makoto Matsumoto, and a report on more recent developments. One focus will be on the structure of the tannakian fundamental group of the category of mixed elliptic motives over M1,1. In particular, we will explain that it is an extension of GL2 by a prounipotent group whose Lie algebra is generated by Eisenstein series and has non-trivial relations coming from cusp forms. We will also discuss the relation of mixed elliptic motives to mixed Tate motives via specialization to the Tate curve and the nodal cubic.
  • Published: 2014
  • Publisher: Institut des Hautes Études Scientifiques (IHÉS)
  • Language: English
1:29:23 Institut des Hautes Études Scientifiques (IHÉS) English 2014

1/6 Nilsequences

Classical Fourier analysis has found many uses in additive number theory. However, while it is well-adapted to some pro - blems, it is unable to handle others. For example, if one has a set A, and one wishes to know how many 3-term arithmetic progressions are contained in A, then Fourier analysis is useful, but if one wishes to count 4-term progressions then it is not. For this, and other, problems the more general notion of a nilsequence is required. NIlsequences are a kind of «higher order character» forming the basis of what is becoming known as «higher-order Fourier analysis». The talks will be about this theory.
  • Published: 2014
  • Publisher: Institut des Hautes Études Scientifiques (IHÉS)
  • Language: English
1:09:42 Institut des Hautes Études Scientifiques (IHÉS) English 2014

2/6 Nilsequences

Classical Fourier analysis has found many uses in additive number theory. However, while it is well-adapted to some pro - blems, it is unable to handle others. For example, if one has a set A, and one wishes to know how many 3-term arithmetic progressions are contained in A, then Fourier analysis is useful, but if one wishes to count 4-term progressions then it is not. For this, and other, problems the more general notion of a nilsequence is required. NIlsequences are a kind of «higher order character» forming the basis of what is becoming known as «higher-order Fourier analysis». The talks will be about this theory.
  • Published: 2014
  • Publisher: Institut des Hautes Études Scientifiques (IHÉS)
  • Language: English
1:25:04 Institut des Hautes Études Scientifiques (IHÉS) English 2014

6/6 Nilsequences

Classical Fourier analysis has found many uses in additive number theory. However, while it is well-adapted to some pro - blems, it is unable to handle others. For example, if one has a set A, and one wishes to know how many 3-term arithmetic progressions are contained in A, then Fourier analysis is useful, but if one wishes to count 4-term progressions then it is not. For this, and other, problems the more general notion of a nilsequence is required. NIlsequences are a kind of «higher order character» forming the basis of what is becoming known as «higher-order Fourier analysis». The talks will be about this theory.
  • Published: 2014
  • Publisher: Institut des Hautes Études Scientifiques (IHÉS)
  • Language: English
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