Title    name Lastest   |   Most hits   년도선택 최근 50건2012201120102009200820072006200520042003200220012000     ASARC Seminar Generic Inner Projections and the Positivity of Double Point Divisors III Atsushi Noma (Yokohama National University) 2012-02-11    For smooth projective variety, it is well-known that the linear system of the double point divisors associated with generic projections is base-point-free. The purpose of this lecture is to study further positivity of the divisors. To this purpose, we study generic inner projecions of (not necessarily smooth) projective varieties.   ASARC Seminar Generic Inner Projections and the Positivity of Double Point Divisors II Atsushi Noma (Yokohama National University) 2012-02-10    For smooth projective variety, it is well-known that the linear system of the double point divisors associated with generic projections is base-point-free. The purpose of this lecture is to study further positivity of the divisors. To this purpose, we study generic inner projecions of (not necessarily smooth) projective varieties.   ASARC Seminar Generic Inner Projections and the Positivity of Double Point Divisors I Atsushi Noma (Yokohama National University) 2012-02-09    For smooth projective variety, it is well-known that the linear system of the double point divisors associated with generic projections is base-point-free. The purpose of this lecture is to study further positivity of the divisors. To this purpose, we study generic inner projecions of (not necessarily smooth) projective varieties.   ASARC Seminar The gamma filtration on projective homogeneous varieties Baek, Sanghoon (University of Ottawa) 2012-02-07   We introduce the notion of essential dimension and discuss how to compute this invariant. In particular, we also explain some recent results on the essential dimension of certain classes of algebras.   ASARC Seminar Essential dimension of algebraic structures Baek, Sanghoon (University of Ottawa) 2012-02-06   We introduce the notion of essential dimension and discuss how to compute this invariant. In particular, we also explain some recent results on the essential dimension of certain classes of algebras.   ASARC Seminar Generic initial ideal theory and its applications IV Aldo Conca (University of Genova) 2012-02-03    The Koszul complex is perhaps the most important complex in commutative algebra. Its most striking features are its algebra structure, its grade-sensitivity and its relations with syzygies. Koszul cycles and homology themselves have an algebra structure. In a regular local ring or in a polynomial ring the Koszul complex of the maximal (homogeneous) ideal gives a resolution of the residue field. In a non-regular ring the residue field has an infinite resolution (which has also an algebra structure)   ASARC Seminar Generic initial ideal theory and its applications III Aldo Conca (University of Genova) 2012-02-02    The Koszul complex is perhaps the most important complex in commutative algebra. Its most striking features are its algebra structure, its grade-sensitivity and its relations with syzygies. Koszul cycles and homology themselves have an algebra structure. In a regular local ring or in a polynomial ring the Koszul complex of the maximal (homogeneous) ideal gives a resolution of the residue field. In a non-regular ring the residue field has an infinite resolution (which has also an algebra structure)   ASARC Seminar Kosniowski conjecture and unitary toric manifolds Zhi Lu (Fudan University) 2012-02-01     ASARC Seminar Schubert Calculus Haibao Duan (Chinese Academy of Sciences) 2012-02-01      ASARC Seminar Schubert Calculus Haibao Duan (Chinese Academy of Sciences) 2012-01-30      ASARC Seminar Generic initial ideal theory and its applications II Aldo Conca (University of Genova) 2012-01-26    The Koszul complex is perhaps the most important complex in commutative algebra. Its most striking features are its algebra structure, its grade-sensitivity and its relations with syzygies. Koszul cycles and homology themselves have an algebra structure. In a regular local ring or in a polynomial ring the Koszul complex of the maximal (homogeneous) ideal gives a resolution of the residue field. In a non-regular ring the residue field has an infinite resolution (which has also an algebra structure)   ASARC Seminar Generic initial ideal theory and its applications I Aldo Conca (University of Genova) 2012-01-25    The Koszul complex is perhaps the most important complex in commutative algebra. Its most striking features are its algebra structure, its grade-sensitivity and its relations with syzygies. Koszul cycles and homology themselves have an algebra structure. In a regular local ring or in a polynomial ring the Koszul complex of the maximal (homogeneous) ideal gives a resolution of the residue field. In a non-regular ring the residue field has an infinite resolution (which has also an algebra structure)   ASARC Seminar Powers of 2 in modular degrees of modular abelian varieties Srilakshmi Krishnamoorthy (IMSc, India) 2012-01-04     ASARC Seminar Intensive Lectures series(6)- GKM theory and equivariant Schubert calculus 6 Megumi Harada (McMaster University) 2011-11-16    This will be a series of roughly 6-8 lectures. The first half will be on well-known and classical material on equivariant cohomology and Schubert calculus, while I will concentrate on my recent joint work with Tymoczko, Bayegan, and Dewitt in the second half of the lecture series. In the very first lecture, I intend to give a very introductory overview lecture on Schubert calculus, concentrating on the most classical case: that of the (cohomology of the) Grassmannian of k-planes in complex n-space. This lecture will be elementary, requiring (mostly) only undergraduate material (mainly linear algebra), but I hope to give the broad overview of a beautiful and elegant subject where algebra, combinatorics, and geometry come together. It will serve as a motivation for the entire lecture series. In the next lecture(s), I intend to give a broad overview of the theory of equivariant cohomology and, in particular, the so-called `GKM' (Goresky-Kottwitz-MacPherson) theory which gives, under suitable conditions, a combinatorial description of the equivariant cohomology in terms of the data of the equivariant 1-skeleton of a space equipped with a group action. I will also discuss some of the Morse-theoretic interpretations of aspects of GKM theory, and in particular take some time to discuss how GKM theory provides a good technology for constructing computationally convenient module bases for equivariant cohomology. In a following lecture(s) I will review the basic geometry of flag varieties associated to compact Lie groups (or complex reductive algebraic groups), including the description of the Schubert varieties sitting inside the flag varieties. I will also briefly recall the corresponding objects in equivariant cohomology, namely the Schubert classes. I will briefly describe some of the known formulas for computing products of certain of these classes. Finally, I will explain some Bruhat-order combinatorics and the Sara Billey formula for computing localizations of Schubert classes at T-fixed points, and how this is another method for a computation `in principle' of the structure constants in the equivariant cohomology ring. In the next lecture(s) I will describe in some detail my recent work with Julianna Tymoczko and Darius Bayegan, in which we generalize classical Schubert calculus to a certain class of subvarieties of flag varieties, namely, the Peterson varieties. We exploit the GKM theory on the ambient flag variety in order to derive a computationally convenient module basis for the S^1-equivariant cohomology ring of Peterson varieties. I will explain in detail how this is done, and also explain some consequences of our approach: namely, Tymoczko and I derive a manifestly-positive and manifestly-integral Monk formula for the structure constants, and Bayegan and I similarly derive a Giambelli formula. In the following lecture(s) I will explain how to generalize the techniques in my work with Tymoczko-Bayegan on Peterson varieties. In particular I explain the key new concept of `GKM-compatible subspaces' of an ambient GKM space. The crucial idea is that, although a subspace X of a GKM space Y may not be itself GKM, the inclusion map of X into Y (and associated map on equivariant cohomology) may have good enough properties that we can deduce properties about the equivariant geometry of X through the GKM theory on Y. Motivated by the notion of GKM-compatibility, Tymoczko and I also introduce a new combinatorial game called `poset pinball', which in some situations allow us to explicitly build computationally convenient module bases analogous to the Schubert classes in Schubert calculus. In the last lecture(s) I will explain concrete examples and applications of the general techniques of GKM-compatibility and poset pinball introduced above, which are contained in my joint work with Tymoczko, Bayegan, and Dewitt. For example, we give an explicit construction of an equivariant lift of the classical Springer action on the cohomology of subregular Springer varieties of type A.   ASARC Seminar Intensive Lectures series(5)- GKM theory and equivariant Schubert calculus 5 Megumi Harada (McMaster University) 2011-11-15   This will be a series of roughly 6-8 lectures. The first half will be on well-known and classical material on equivariant cohomology and Schubert calculus, while I will concentrate on my recent joint work with Tymoczko, Bayegan, and Dewitt in the second half of the lecture series. In the very first lecture, I intend to give a very introductory overview lecture on Schubert calculus, concentrating on the most classical case: that of the (cohomology of the) Grassmannian of k-planes in complex n-space. This lecture will be elementary, requiring (mostly) only undergraduate material (mainly linear algebra), but I hope to give the broad overview of a beautiful and elegant subject where algebra, combinatorics, and geometry come together. It will serve as a motivation for the entire lecture series. In the next lecture(s), I intend to give a broad overview of the theory of equivariant cohomology and, in particular, the so-called `GKM' (Goresky-Kottwitz-MacPherson) theory which gives, under suitable conditions, a combinatorial description of the equivariant cohomology in terms of the data of the equivariant 1-skeleton of a space equipped with a group action. I will also discuss some of the Morse-theoretic interpretations of aspects of GKM theory, and in particular take some time to discuss how GKM theory provides a good technology for constructing computationally convenient module bases for equivariant cohomology. In a following lecture(s) I will review the basic geometry of flag varieties associated to compact Lie groups (or complex reductive algebraic groups), including the description of the Schubert varieties sitting inside the flag varieties. I will also briefly recall the corresponding objects in equivariant cohomology, namely the Schubert classes. I will briefly describe some of the known formulas for computing products of certain of these classes. Finally, I will explain some Bruhat-order combinatorics and the Sara Billey formula for computing localizations of Schubert classes at T-fixed points, and how this is another method for a computation `in principle' of the structure constants in the equivariant cohomology ring. In the next lecture(s) I will describe in some detail my recent work with Julianna Tymoczko and Darius Bayegan, in which we generalize classical Schubert calculus to a certain class of subvarieties of flag varieties, namely, the Peterson varieties. We exploit the GKM theory on the ambient flag variety in order to derive a computationally convenient module basis for the S^1-equivariant cohomology ring of Peterson varieties. I will explain in detail how this is done, and also explain some consequences of our approach: namely, Tymoczko and I derive a manifestly-positive and manifestly-integral Monk formula for the structure constants, and Bayegan and I similarly derive a Giambelli formula. In the following lecture(s) I will explain how to generalize the techniques in my work with Tymoczko-Bayegan on Peterson varieties. In particular I explain the key new concept of `GKM-compatible subspaces' of an ambient GKM space. The crucial idea is that, although a subspace X of a GKM space Y may not be itself GKM, the inclusion map of X into Y (and associated map on equivariant cohomology) may have good enough properties that we can deduce properties about the equivariant geometry of X through the GKM theory on Y. Motivated by the notion of GKM-compatibility, Tymoczko and I also introduce a new combinatorial game called `poset pinball', which in some situations allow us to explicitly build computationally convenient module bases analogous to the Schubert classes in Schubert calculus. In the last lecture(s) I will explain concrete examples and applications of the general techniques of GKM-compatibility and poset pinball introduced above, which are contained in my joint work with Tymoczko, Bayegan, and Dewitt. For example, we give an explicit construction of an equivariant lift of the classical Springer action on the cohomology of subregular Springer varieties of type A.   ASARC Seminar Volume conjecture and extended Bloch group Cho, Jinseok (KIAS) 2011-11-15   Kashaev volume conjecture suggests that the limit of the colored Jones polynomial of a hyperbolic knot gives the volume and the Chern-Simons invariant of the knot complement. It is one of the most important problems in quantum topology because it shows many non-trivial relations between many areas including knot theory, hyperbolic geometry, quantum group, extended Bloch group, and more. In this talk, we survey many aspects of the volume conjecture. Especially, we focus on how the extended Bloch group plays a crucial role in proving the optimistic limit version of the volume conjecture.   ASARC Seminar Intensive Lectures series(4)- GKM theory and equivariant Schubert calculus 4 Megumi Harada (McMaster University) 2011-11-14    This will be a series of roughly 6-8 lectures. The first half will be on well-known and classical material on equivariant cohomology and Schubert calculus, while I will concentrate on my recent joint work with Tymoczko, Bayegan, and Dewitt in the second half of the lecture series. In the very first lecture, I intend to give a very introductory overview lecture on Schubert calculus, concentrating on the most classical case: that of the (cohomology of the) Grassmannian of k-planes in complex n-space. This lecture will be elementary, requiring (mostly) only undergraduate material (mainly linear algebra), but I hope to give the broad overview of a beautiful and elegant subject where algebra, combinatorics, and geometry come together. It will serve as a motivation for the entire lecture series. In the next lecture(s), I intend to give a broad overview of the theory of equivariant cohomology and, in particular, the so-called `GKM' (Goresky-Kottwitz-MacPherson) theory which gives, under suitable conditions, a combinatorial description of the equivariant cohomology in terms of the data of the equivariant 1-skeleton of a space equipped with a group action. I will also discuss some of the Morse-theoretic interpretations of aspects of GKM theory, and in particular take some time to discuss how GKM theory provides a good technology for constructing computationally convenient module bases for equivariant cohomology. In a following lecture(s) I will review the basic geometry of flag varieties associated to compact Lie groups (or complex reductive algebraic groups), including the description of the Schubert varieties sitting inside the flag varieties. I will also briefly recall the corresponding objects in equivariant cohomology, namely the Schubert classes. I will briefly describe some of the known formulas for computing products of certain of these classes. Finally, I will explain some Bruhat-order combinatorics and the Sara Billey formula for computing localizations of Schubert classes at T-fixed points, and how this is another method for a computation `in principle' of the structure constants in the equivariant cohomology ring. In the next lecture(s) I will describe in some detail my recent work with Julianna Tymoczko and Darius Bayegan, in which we generalize classical Schubert calculus to a certain class of subvarieties of flag varieties, namely, the Peterson varieties. We exploit the GKM theory on the ambient flag variety in order to derive a computationally convenient module basis for the S^1-equivariant cohomology ring of Peterson varieties. I will explain in detail how this is done, and also explain some consequences of our approach: namely, Tymoczko and I derive a manifestly-positive and manifestly-integral Monk formula for the structure constants, and Bayegan and I similarly derive a Giambelli formula. In the following lecture(s) I will explain how to generalize the techniques in my work with Tymoczko-Bayegan on Peterson varieties. In particular I explain the key new concept of `GKM-compatible subspaces' of an ambient GKM space. The crucial idea is that, although a subspace X of a GKM space Y may not be itself GKM, the inclusion map of X into Y (and associated map on equivariant cohomology) may have good enough properties that we can deduce properties about the equivariant geometry of X through the GKM theory on Y. Motivated by the notion of GKM-compatibility, Tymoczko and I also introduce a new combinatorial game called `poset pinball', which in some situations allow us to explicitly build computationally convenient module bases analogous to the Schubert classes in Schubert calculus. In the last lecture(s) I will explain concrete examples and applications of the general techniques of GKM-compatibility and poset pinball introduced above, which are contained in my joint work with Tymoczko, Bayegan, and Dewitt. For example, we give an explicit construction of an equivariant lift of the classical Springer action on the cohomology of subregular Springer varieties of type A.   ASARC Seminar Intensive Lectures series(3)- GKM theory and equivariant Schubert calculus 3 Megumi Harada (McMaster University) 2011-11-11    This will be a series of roughly 6-8 lectures. The first half will be on well-known and classical material on equivariant cohomology and Schubert calculus, while I will concentrate on my recent joint work with Tymoczko, Bayegan, and Dewitt in the second half of the lecture series. In the very first lecture, I intend to give a very introductory overview lecture on Schubert calculus, concentrating on the most classical case: that of the (cohomology of the) Grassmannian of k-planes in complex n-space. This lecture will be elementary, requiring (mostly) only undergraduate material (mainly linear algebra), but I hope to give the broad overview of a beautiful and elegant subject where algebra, combinatorics, and geometry come together. It will serve as a motivation for the entire lecture series. In the next lecture(s), I intend to give a broad overview of the theory of equivariant cohomology and, in particular, the so-called `GKM' (Goresky-Kottwitz-MacPherson) theory which gives, under suitable conditions, a combinatorial description of the equivariant cohomology in terms of the data of the equivariant 1-skeleton of a space equipped with a group action. I will also discuss some of the Morse-theoretic interpretations of aspects of GKM theory, and in particular take some time to discuss how GKM theory provides a good technology for constructing computationally convenient module bases for equivariant cohomology. In a following lecture(s) I will review the basic geometry of flag varieties associated to compact Lie groups (or complex reductive algebraic groups), including the description of the Schubert varieties sitting inside the flag varieties. I will also briefly recall the corresponding objects in equivariant cohomology, namely the Schubert classes. I will briefly describe some of the known formulas for computing products of certain of these classes. Finally, I will explain some Bruhat-order combinatorics and the Sara Billey formula for computing localizations of Schubert classes at T-fixed points, and how this is another method for a computation `in principle' of the structure constants in the equivariant cohomology ring. In the next lecture(s) I will describe in some detail my recent work with Julianna Tymoczko and Darius Bayegan, in which we generalize classical Schubert calculus to a certain class of subvarieties of flag varieties, namely, the Peterson varieties. We exploit the GKM theory on the ambient flag variety in order to derive a computationally convenient module basis for the S^1-equivariant cohomology ring of Peterson varieties. I will explain in detail how this is done, and also explain some consequences of our approach: namely, Tymoczko and I derive a manifestly-positive and manifestly-integral Monk formula for the structure constants, and Bayegan and I similarly derive a Giambelli formula. In the following lecture(s) I will explain how to generalize the techniques in my work with Tymoczko-Bayegan on Peterson varieties. In particular I explain the key new concept of `GKM-compatible subspaces' of an ambient GKM space. The crucial idea is that, although a subspace X of a GKM space Y may not be itself GKM, the inclusion map of X into Y (and associated map on equivariant cohomology) may have good enough properties that we can deduce properties about the equivariant geometry of X through the GKM theory on Y. Motivated by the notion of GKM-compatibility, Tymoczko and I also introduce a new combinatorial game called `poset pinball', which in some situations allow us to explicitly build computationally convenient module bases analogous to the Schubert classes in Schubert calculus. In the last lecture(s) I will explain concrete examples and applications of the general techniques of GKM-compatibility and poset pinball introduced above, which are contained in my joint work with Tymoczko, Bayegan, and Dewitt. For example, we give an explicit construction of an equivariant lift of the classical Springer action on the cohomology of subregular Springer varieties of type A.   ASARC Seminar Intensive Lectures series(2)- GKM theory and equivariant Schubert calculus 2 Megumi Harada (McMaster University) 2011-11-10    This will be a series of roughly 6-8 lectures. The first half will be on well-known and classical material on equivariant cohomology and Schubert calculus, while I will concentrate on my recent joint work with Tymoczko, Bayegan, and Dewitt in the second half of the lecture series. In the very first lecture, I intend to give a very introductory overview lecture on Schubert calculus, concentrating on the most classical case: that of the (cohomology of the) Grassmannian of k-planes in complex n-space. This lecture will be elementary, requiring (mostly) only undergraduate material (mainly linear algebra), but I hope to give the broad overview of a beautiful and elegant subject where algebra, combinatorics, and geometry come together. It will serve as a motivation for the entire lecture series. In the next lecture(s), I intend to give a broad overview of the theory of equivariant cohomology and, in particular, the so-called `GKM' (Goresky-Kottwitz-MacPherson) theory which gives, under suitable conditions, a combinatorial description of the equivariant cohomology in terms of the data of the equivariant 1-skeleton of a space equipped with a group action. I will also discuss some of the Morse-theoretic interpretations of aspects of GKM theory, and in particular take some time to discuss how GKM theory provides a good technology for constructing computationally convenient module bases for equivariant cohomology. In a following lecture(s) I will review the basic geometry of flag varieties associated to compact Lie groups (or complex reductive algebraic groups), including the description of the Schubert varieties sitting inside the flag varieties. I will also briefly recall the corresponding objects in equivariant cohomology, namely the Schubert classes. I will briefly describe some of the known formulas for computing products of certain of these classes. Finally, I will explain some Bruhat-order combinatorics and the Sara Billey formula for computing localizations of Schubert classes at T-fixed points, and how this is another method for a computation `in principle' of the structure constants in the equivariant cohomology ring. In the next lecture(s) I will describe in some detail my recent work with Julianna Tymoczko and Darius Bayegan, in which we generalize classical Schubert calculus to a certain class of subvarieties of flag varieties, namely, the Peterson varieties. We exploit the GKM theory on the ambient flag variety in order to derive a computationally convenient module basis for the S^1-equivariant cohomology ring of Peterson varieties. I will explain in detail how this is done, and also explain some consequences of our approach: namely, Tymoczko and I derive a manifestly-positive and manifestly-integral Monk formula for the structure constants, and Bayegan and I similarly derive a Giambelli formula. In the following lecture(s) I will explain how to generalize the techniques in my work with Tymoczko-Bayegan on Peterson varieties. In particular I explain the key new concept of `GKM-compatible subspaces' of an ambient GKM space. The crucial idea is that, although a subspace X of a GKM space Y may not be itself GKM, the inclusion map of X into Y (and associated map on equivariant cohomology) may have good enough properties that we can deduce properties about the equivariant geometry of X through the GKM theory on Y. Motivated by the notion of GKM-compatibility, Tymoczko and I also introduce a new combinatorial game called `poset pinball', which in some situations allow us to explicitly build computationally convenient module bases analogous to the Schubert classes in Schubert calculus. In the last lecture(s) I will explain concrete examples and applications of the general techniques of GKM-compatibility and poset pinball introduced above, which are contained in my joint work with Tymoczko, Bayegan, and Dewitt. For example, we give an explicit construction of an equivariant lift of the classical Springer action on the cohomology of subregular Springer varieties of type A.   ASARC Seminar Intensive Lectures series(1)- GKM theory and equivariant Schubert calculus 1 Megumi Harada (McMaster University) 2011-11-09   This will be a series of roughly 6-8 lectures. The first half will be on well-known and classical material on equivariant cohomology and Schubert calculus, while I will concentrate on my recent joint work with Tymoczko, Bayegan, and Dewitt in the second half of the lecture series. In the very first lecture, I intend to give a very introductory overview lecture on Schubert calculus, concentrating on the most classical case: that of the (cohomology of the) Grassmannian of k-planes in complex n-space. This lecture will be elementary, requiring (mostly) only undergraduate material (mainly linear algebra), but I hope to give the broad overview of a beautiful and elegant subject where algebra, combinatorics, and geometry come together. It will serve as a motivation for the entire lecture series. In the next lecture(s), I intend to give a broad overview of the theory of equivariant cohomology and, in particular, the so-called `GKM' (Goresky-Kottwitz-MacPherson) theory which gives, under suitable conditions, a combinatorial description of the equivariant cohomology in terms of the data of the equivariant 1-skeleton of a space equipped with a group action. I will also discuss some of the Morse-theoretic interpretations of aspects of GKM theory, and in particular take some time to discuss how GKM theory provides a good technology for constructing computationally convenient module bases for equivariant cohomology. In a following lecture(s) I will review the basic geometry of flag varieties associated to compact Lie groups (or complex reductive algebraic groups), including the description of the Schubert varieties sitting inside the flag varieties. I will also briefly recall the corresponding objects in equivariant cohomology, namely the Schubert classes. I will briefly describe some of the known formulas for computing products of certain of these classes. Finally, I will explain some Bruhat-order combinatorics and the Sara Billey formula for computing localizations of Schubert classes at T-fixed points, and how this is another method for a computation `in principle' of the structure constants in the equivariant cohomology ring. In the next lecture(s) I will describe in some detail my recent work with Julianna Tymoczko and Darius Bayegan, in which we generalize classical Schubert calculus to a certain class of subvarieties of flag varieties, namely, the Peterson varieties. We exploit the GKM theory on the ambient flag variety in order to derive a computationally convenient module basis for the S^1-equivariant cohomology ring of Peterson varieties. I will explain in detail how this is done, and also explain some consequences of our approach: namely, Tymoczko and I derive a manifestly-positive and manifestly-integral Monk formula for the structure constants, and Bayegan and I similarly derive a Giambelli formula. In the following lecture(s) I will explain how to generalize the techniques in my work with Tymoczko-Bayegan on Peterson varieties. In particular I explain the key new concept of `GKM-compatible subspaces' of an ambient GKM space. The crucial idea is that, although a subspace X of a GKM space Y may not be itself GKM, the inclusion map of X into Y (and associated map on equivariant cohomology) may have good enough properties that we can deduce properties about the equivariant geometry of X through the GKM theory on Y. Motivated by the notion of GKM-compatibility, Tymoczko and I also introduce a new combinatorial game called `poset pinball', which in some situations allow us to explicitly build computationally convenient module bases analogous to the Schubert classes in Schubert calculus. In the last lecture(s) I will explain concrete examples and applications of the general techniques of GKM-compatibility and poset pinball introduced above, which are contained in my joint work with Tymoczko, Bayegan, and Dewitt. For example, we give an explicit construction of an equivariant lift of the classical Springer action on the cohomology of subregular Springer varieties of type A.   ASARC Seminar Affine embeddings of reductive groups Hyun, Yoonsuk (KIAS) 2011-11-08   In this seminar, I will talk about the properties and the classification of embeddings of homogeneous spaces, especially the case of affine normal embeddings of reductive groups. We might guess that as in the case of toric varieties, some specific subset of one-parameter subgroups may contribute to the classification of affine embeddings of general reductive group. To check this, we review the theory of affine normal SL(2)-embeddings, and prove that the classification cannot be solved entirely based on one-parameter subgroups. We can also observe that even though this set does not give a complete answer to the classification problem, but still contains useful information about varieties. If time permitted, I will also give examples of GL(2)-embeddings which had not previously been constructed in detail, which might be helpful in understanding the general classification of affine normal G-embeddings.   ASARC Seminar Degenerations of Mixed Hodge Structure from a Tanakian viewpoint Patrick Brosnan (University of Maryland) 2011-09-16   Deligne observed a long time ago that the category of split real Hodge structures is equivalent to the category of representations of a certain rank 2 torus. Later he described the Tanakian Galois group of the category of all real mixed Hodge structures as a certain extension of this torus. I'll discuss this and joint work with Greg Pearlstein where we spell out a similar picture for degenerations of real mixed Hodge structure.   ASARC Seminar Weak Northcott property and the D-ratio for rational maps Lee, Chonggyu (University of Illinois at Chicago) 2011-08-04   In 1950, Northcott proved the height inequality for morphisms on projective spaces. Let f:Pn→Pn be a morphism. Then, there is a constant Cdepending on the given morphism such that the height function h satisfies h(f(P))+C>degfh(P)>h(f(P))-C for all points P∈Pn. Unfortunately, the upper bound of the inequality does not hold for rational maps. However, we can find weaker inequality by 1) restricting points on an affine open set and 2) enlarging the upper bound a little bit. In this talk, I will introduce the D-ratio for a rational map on projective spaces and prove the Weak Northcott property for rational maps.   ASARC Seminar Orbifolds and Equivariant Geometry Tomoo Matsumura (Cornell University) 2011-06-27   There are three ways to define an orbifold: orbifolds charts, groupoids, stacks. I will explain these notions in smooth category by working out a few basic examples. It will be one of the goals of the talk to give some understanding of the notion of stacks, which is an important language to study moduli problems and also an orbifold as a presentation-free intrinsic object. If time allows, I will get to the definitions of group actions on orbifolds and the (equivariant) cohomology over integer coefficients.   ASARC Seminar Classification of equivariant vector bundles over two-sphere Kim, Minkyu (Gyeongin National University of Education) 2011-06-03   We classify equivariant topological complex vector bundles over two-sphere under a compact Lie group (not necessarily effective) action. It is shown that nonequivariant Chern classes and isotropy representations at (at most) three points are sufficient to classify equivariant vector bundles except a few cases.   ASARC Seminar Hilbert scheme of points. Mini lecture III Lee, Hwayoung (KIAS) 2011-05-17   Hilbert scheme of points에 대한 정리들과 예들을 소개하고, Hilbert scheme의 scheme structre를 국소적으로는 어떻게 결정하는지에 대한, 즉 Deformation과 관련된 구체적인 계산을 보여줍니다.   ASARC Seminar Hilbert scheme of points. Mini lecture II Lee, Hwayoung (KIAS) 2011-05-11   Hilbert scheme of points에 대한 정리들과 예들을 소개하고, Hilbert scheme의 scheme structre를 국소적으로는 어떻게 결정하는지에 대한, 즉 Deformation과 관련된 구체적인 계산을 보여줍니다.   ASARC Seminar Hilbert scheme of points. Mini lecture I Lee, Hwayoung (KIAS) 2011-05-03   Hilbert scheme of points에 대한 정리들과 예들을 소개하고, Hilbert scheme의 scheme structre를 국소적으로는 어떻게 결정하는지에 대한, 즉 Deformation과 관련된 구체적인 계산을 보여줍니다.   ASARC Seminar A bound on the degree of scheme defined by quadratic equations José Carlos Sierra (ICMAT) 2011-04-15      ASARC Seminar On the quadratic normality and the triple curve of 3-dimensional subvarieties of P^5 José Carlos Sierra (ICMAT) 2011-04-13      ASARC Seminar Tangential projections and secant defective varieties José Carlos Sierra (ICMAT) 2011-04-12      ASARC Seminar Intensive lectures on projective geometry IV-Manifolds covered by lines Paltin Ionescu (University of Bucharest) 2011-03-28    This is a common generalisation of the special manifolds encountered previously. We shall see some fundamental principles and expected classification results about them.   ASARC Seminar Intensive lectures on projective geometry III-Defective manifolds Paltin Ionescu (University of Bucharest) 2011-03-25    There are two kinds of such: secant defective and dual defective. We shall investigate both and see that they are actually related.   ASARC Seminar Intensive lectures on projective geometry II-Manifolds of VERY small codimension Paltin Ionescu (University of Bucharest) 2011-03-23    Keeping the previous notation, these satisfy the stronger condition n>=2c+1.Here we will talk about special cases of the (in)famous Hartshorne Conjecture. Lecture III: Defective manifolds. There are two kinds of such: secant defective and dual defective. We shall investigate both and see that they are actually related.   ASARC Seminar Intensive lectures on projective geometry I-Manifolds of small codimension Paltin Ionescu (University of Bucharest) 2011-03-22    These are embedded projective manifolds of dimension n and codimension c, such that n>=c. They have many remarkable topological and geometrical properties. Classification results are possible for the   ASARC Seminar On the coefficients of weakly holomorphic Drinfeld modular forms Choi, Soyoung (Dongguk University) 2010-12-03   We construct a basis the space of weakly holomorphic Drinfeld modular forms.and observe some arithmetic properties of coefficients of the basis elements. Precisely we find that the basis elements satisty some generating function and find some duality between coefficients of the basis elements.   ASARC Seminar Results on geometric flow Pak Tung Ho (Sogang University) 2010-10-26   I will talk about several results on geometric flow. In particular, I will talk about prescribed (Gaussian) curvature flow, CR Yamabe flow, and Q-curvature flow.   ASARC Seminar Finite generation questions for motivic cohomology Thomas Geisser (U. Southern California / Nagoya University) 2010-10-05     ASARC Seminar A Quantum Kirwan Map and Symplectic Vortices Fabian Ziltener (KIAS) 2010-09-15   Given a Hamiltonian Lie group action on a symplectic manifold, I will explain the construction of a quantum deformation of the Kirwan map. It is defined by counting solutions of the symplectic vortex equations, which are a gauge theoretical deformation of the Cauchy-Riemann equations. Based on this map, I will formulate a quantum abelianization conjecture (joint work with Chris Woodward).   ASARC Seminar Estimates of the topological entropy from below for continuous self-maps on some compact manifolds Waclaw Marzantowicz (UAM Poznan) 2010-09-10   We confirm that Entropy Conjecture holds for every continuous self-map of a compact K( π, 1) manifold with the fund. gr. π virtually nilpotent, e.g. for every continuous map of an infra-nilmanifold. In fact, a lower estimate of the topological entropy by the logarithm of the spectral radius of exterior power of an assoc. ”linearization matrix” with integer entries. This & estimates of Mahler measure of polynom., give some absolute lower bounds for the entropy.   ASARC Seminar Recent progress on algebraic cycles Masanori Asakura (Hokkaido University) 2010-08-31   It is an important conjecture that the Chow group of a smooth projective variety over a number field is a finitely generated Z-module, and no one knows how to solve it so far. On the other hand people considered two modified questions which are more accessible. One is whether the Chow group modulo n is finite or not, and the other is whether the torsion part is finite or not.   ASARC Seminar Quasitoric orbifolds 2 Mainak Poddar (Indian Statistical Institute) 2010-05-27    We will define quasitoric orbifolds, describe their topological invariants. We will discuss almost complex structures and blowdowns on four dimensional quasitoric orbifolds and a McKay correspondence for these.   ASARC Seminar Quasitoric orbifolds 1 Mainak Poddar (Indian Statistical Institute) 2010-05-27   We will define quasitoric orbifolds, describe their topological invariants. We will discuss almost complex structures and blowdowns on four dimensional quasitoric orbifolds and a McKay correspondence for these.   ASARC Seminar Stringy topology of orbifolds 2 Mainak Poddar (Indian Statistical Institute) 2010-05-25    We will discuss basic facts about differentiable orbifolds and intorduce Chen-Ruan cohomology groups and Mckay correspondence.   ASARC Seminar Stringy topology of orbifolds 1 Mainak Poddar (Indian Statistical Institute) 2010-05-25   We will discuss basic facts about differentiable orbifolds and intorduce Chen-Ruan cohomology groups and Mckay correspondence.   ASARC Seminar Non-commutative topology and geometry: a geometry-algebra correspondence. Lee, Hyunho (Seoul National University) 2010-05-25   Many interesting works on topological algebras are best understood in view of algebraic topology or diffrential geometry. Since Gelfand-Naimark's celebrated characterization of commutative C*-algebras as a dual of locally compact Hausdorff space, the category of non-commutative C*-algebras has been regarded as "non-commutative locally compact Hausdorff spaces". In this talk, he will introduce so called non-commutative (algebraic) topology and (differential) geometry relying on his own appreciations of the subjects.   ASARC Seminar Holomorphic Lagrangian fibrations. Justin Sawon (University of North Carolina - Chapel Hill) 2010-05-11   The only possible fibration on a K3 surface is an elliptic fibration, with base P^1. Lagrangian fibrations on holomorphic symplectic manifolds are higher-dimensional generalizations of elliptic K3 surfaces. In this talk I will describe some results about Lagrangian fibrations concerning their bases, discriminant loci, singular fibres, and classifying maps.   ASARC Seminar Infinitesimal deformations of complements of plumbings. Shin, Dongsoo (Chungnam National University) 2010-05-04   We shall construct infinitesimal deformations of a complex surface with boundary, which is the complement of a tubular neighborhood of a special linear chain of smooth rational curves. We show that the deformation induces a non-trivial deformation of the complex structure on some divisor on Y.   ASARC Seminar Young tableaux and crystals 3 Kang, Seokjin (Seoul National University) 2010-04-23    Contents: 1) General linear Lie algebras 2) Crystals 3) Young tableaux 4) Insertion scheme   ASARC Seminar Young tableaux and crystals 2 Kang, Seokjin (Seoul National University) 2010-04-22    Contents: 1) General linear Lie algebras 2) Crystals 3) Young tableaux 4) Insertion scheme

Information Center for Mathematical Sciences KAIST 335 Gwahangno (373-1 Guseong-dong), Yuseong-gu, Daejeon 305-701, Republic of Korea TEL +82-42-869-8195~6, FAX +82-42-869-5722, e-mail : mathnet@mathnet.or.kr Copyright (c) 2009 by ICMS. All Rights Reserved