Cookies

We use cookies to ensure that we give you the best experience on our website. You can change your cookie settings at any time. Otherwise, we'll assume you're OK to continue.

Department of Mathematical Sciences

Research Seminar Series

Applied Mathematics Seminars

Pure Maths Colloquium: The disparity between smooth and topologically slice knots

Presented by Min Hoon Kim, KIAS

2 October 2017 16:00 in CM221

Understanding the subtle difference between the topological and smooth categories is a central subject in 4-manifold topology. The local difference in the categories can be studied through knot theory. A knot in the 3-sphere is called smoothly slice (respectively, topologically slice) if it bounds a smoothly embedded (respectively, topologically embedded, locally flat) disc in the 4-ball.

After Casson used the celebrated results of Freedman and Donaldson on 4-dimensional manifolds to find a topologically slice knot that is not smoothly slice, distinguishing topologically slice knots and smoothly slice knots has been extensively studied.

In 2012, in order to try to introduce some structure into the problem, Cochran, Harvey and Horn introduced a remarkable framework to study the set (actually a group) of topologically slice knots modulo smoothly slice knots, defining a geometrically inspired filtration, called the bipolar filtration. However a crucial question left unsettled was the non-triviality of the graded quotients. In joint work with Jae Choon Cha, we showed that the graded quotient of the bipolar filtration in fact has infinite rank, at each stage greater than one. In this talk, I will give a friendly, short introduction to knot theory in 3 and 4 dimensions, focussing on the differences between the smooth and topological categories, and I will briefly survey the recent progress on the bipolar filtration.

Contact anna.felikson@durham.ac.uk for more information


Arithmetic Study Group

Pure Maths Colloquium: The disparity between smooth and topologically slice knots

Presented by Min Hoon Kim, KIAS

2 October 2017 16:00 in CM221

Understanding the subtle difference between the topological and smooth categories is a central subject in 4-manifold topology. The local difference in the categories can be studied through knot theory. A knot in the 3-sphere is called smoothly slice (respectively, topologically slice) if it bounds a smoothly embedded (respectively, topologically embedded, locally flat) disc in the 4-ball.

After Casson used the celebrated results of Freedman and Donaldson on 4-dimensional manifolds to find a topologically slice knot that is not smoothly slice, distinguishing topologically slice knots and smoothly slice knots has been extensively studied.

In 2012, in order to try to introduce some structure into the problem, Cochran, Harvey and Horn introduced a remarkable framework to study the set (actually a group) of topologically slice knots modulo smoothly slice knots, defining a geometrically inspired filtration, called the bipolar filtration. However a crucial question left unsettled was the non-triviality of the graded quotients. In joint work with Jae Choon Cha, we showed that the graded quotient of the bipolar filtration in fact has infinite rank, at each stage greater than one. In this talk, I will give a friendly, short introduction to knot theory in 3 and 4 dimensions, focussing on the differences between the smooth and topological categories, and I will briefly survey the recent progress on the bipolar filtration.

Contact anna.felikson@durham.ac.uk for more information


Centre for Particle Theory Colloquia

Pure Maths Colloquium: The disparity between smooth and topologically slice knots

Presented by Min Hoon Kim, KIAS

2 October 2017 16:00 in CM221

Understanding the subtle difference between the topological and smooth categories is a central subject in 4-manifold topology. The local difference in the categories can be studied through knot theory. A knot in the 3-sphere is called smoothly slice (respectively, topologically slice) if it bounds a smoothly embedded (respectively, topologically embedded, locally flat) disc in the 4-ball.

After Casson used the celebrated results of Freedman and Donaldson on 4-dimensional manifolds to find a topologically slice knot that is not smoothly slice, distinguishing topologically slice knots and smoothly slice knots has been extensively studied.

In 2012, in order to try to introduce some structure into the problem, Cochran, Harvey and Horn introduced a remarkable framework to study the set (actually a group) of topologically slice knots modulo smoothly slice knots, defining a geometrically inspired filtration, called the bipolar filtration. However a crucial question left unsettled was the non-triviality of the graded quotients. In joint work with Jae Choon Cha, we showed that the graded quotient of the bipolar filtration in fact has infinite rank, at each stage greater than one. In this talk, I will give a friendly, short introduction to knot theory in 3 and 4 dimensions, focussing on the differences between the smooth and topological categories, and I will briefly survey the recent progress on the bipolar filtration.

Contact anna.felikson@durham.ac.uk for more information


Computing Seminars/Talks

Pure Maths Colloquium: The disparity between smooth and topologically slice knots

Presented by Min Hoon Kim, KIAS

2 October 2017 16:00 in CM221

Understanding the subtle difference between the topological and smooth categories is a central subject in 4-manifold topology. The local difference in the categories can be studied through knot theory. A knot in the 3-sphere is called smoothly slice (respectively, topologically slice) if it bounds a smoothly embedded (respectively, topologically embedded, locally flat) disc in the 4-ball.

After Casson used the celebrated results of Freedman and Donaldson on 4-dimensional manifolds to find a topologically slice knot that is not smoothly slice, distinguishing topologically slice knots and smoothly slice knots has been extensively studied.

In 2012, in order to try to introduce some structure into the problem, Cochran, Harvey and Horn introduced a remarkable framework to study the set (actually a group) of topologically slice knots modulo smoothly slice knots, defining a geometrically inspired filtration, called the bipolar filtration. However a crucial question left unsettled was the non-triviality of the graded quotients. In joint work with Jae Choon Cha, we showed that the graded quotient of the bipolar filtration in fact has infinite rank, at each stage greater than one. In this talk, I will give a friendly, short introduction to knot theory in 3 and 4 dimensions, focussing on the differences between the smooth and topological categories, and I will briefly survey the recent progress on the bipolar filtration.

Contact anna.felikson@durham.ac.uk for more information


CPT Student Seminar

Pure Maths Colloquium: The disparity between smooth and topologically slice knots

Presented by Min Hoon Kim, KIAS

2 October 2017 16:00 in CM221

Understanding the subtle difference between the topological and smooth categories is a central subject in 4-manifold topology. The local difference in the categories can be studied through knot theory. A knot in the 3-sphere is called smoothly slice (respectively, topologically slice) if it bounds a smoothly embedded (respectively, topologically embedded, locally flat) disc in the 4-ball.

After Casson used the celebrated results of Freedman and Donaldson on 4-dimensional manifolds to find a topologically slice knot that is not smoothly slice, distinguishing topologically slice knots and smoothly slice knots has been extensively studied.

In 2012, in order to try to introduce some structure into the problem, Cochran, Harvey and Horn introduced a remarkable framework to study the set (actually a group) of topologically slice knots modulo smoothly slice knots, defining a geometrically inspired filtration, called the bipolar filtration. However a crucial question left unsettled was the non-triviality of the graded quotients. In joint work with Jae Choon Cha, we showed that the graded quotient of the bipolar filtration in fact has infinite rank, at each stage greater than one. In this talk, I will give a friendly, short introduction to knot theory in 3 and 4 dimensions, focussing on the differences between the smooth and topological categories, and I will briefly survey the recent progress on the bipolar filtration.

Contact anna.felikson@durham.ac.uk for more information


Departmental Research Colloquium

Pure Maths Colloquium: The disparity between smooth and topologically slice knots

Presented by Min Hoon Kim, KIAS

2 October 2017 16:00 in CM221

Understanding the subtle difference between the topological and smooth categories is a central subject in 4-manifold topology. The local difference in the categories can be studied through knot theory. A knot in the 3-sphere is called smoothly slice (respectively, topologically slice) if it bounds a smoothly embedded (respectively, topologically embedded, locally flat) disc in the 4-ball.

After Casson used the celebrated results of Freedman and Donaldson on 4-dimensional manifolds to find a topologically slice knot that is not smoothly slice, distinguishing topologically slice knots and smoothly slice knots has been extensively studied.

In 2012, in order to try to introduce some structure into the problem, Cochran, Harvey and Horn introduced a remarkable framework to study the set (actually a group) of topologically slice knots modulo smoothly slice knots, defining a geometrically inspired filtration, called the bipolar filtration. However a crucial question left unsettled was the non-triviality of the graded quotients. In joint work with Jae Choon Cha, we showed that the graded quotient of the bipolar filtration in fact has infinite rank, at each stage greater than one. In this talk, I will give a friendly, short introduction to knot theory in 3 and 4 dimensions, focussing on the differences between the smooth and topological categories, and I will briefly survey the recent progress on the bipolar filtration.

Contact anna.felikson@durham.ac.uk for more information


Distinguished Lectures and Public Lectures

Pure Maths Colloquium: The disparity between smooth and topologically slice knots

Presented by Min Hoon Kim, KIAS

2 October 2017 16:00 in CM221

Understanding the subtle difference between the topological and smooth categories is a central subject in 4-manifold topology. The local difference in the categories can be studied through knot theory. A knot in the 3-sphere is called smoothly slice (respectively, topologically slice) if it bounds a smoothly embedded (respectively, topologically embedded, locally flat) disc in the 4-ball.

After Casson used the celebrated results of Freedman and Donaldson on 4-dimensional manifolds to find a topologically slice knot that is not smoothly slice, distinguishing topologically slice knots and smoothly slice knots has been extensively studied.

In 2012, in order to try to introduce some structure into the problem, Cochran, Harvey and Horn introduced a remarkable framework to study the set (actually a group) of topologically slice knots modulo smoothly slice knots, defining a geometrically inspired filtration, called the bipolar filtration. However a crucial question left unsettled was the non-triviality of the graded quotients. In joint work with Jae Choon Cha, we showed that the graded quotient of the bipolar filtration in fact has infinite rank, at each stage greater than one. In this talk, I will give a friendly, short introduction to knot theory in 3 and 4 dimensions, focussing on the differences between the smooth and topological categories, and I will briefly survey the recent progress on the bipolar filtration.

Contact anna.felikson@durham.ac.uk for more information


Geometry and Topology Seminar

Pure Maths Colloquium: The disparity between smooth and topologically slice knots

Presented by Min Hoon Kim, KIAS

2 October 2017 16:00 in CM221

Understanding the subtle difference between the topological and smooth categories is a central subject in 4-manifold topology. The local difference in the categories can be studied through knot theory. A knot in the 3-sphere is called smoothly slice (respectively, topologically slice) if it bounds a smoothly embedded (respectively, topologically embedded, locally flat) disc in the 4-ball.

After Casson used the celebrated results of Freedman and Donaldson on 4-dimensional manifolds to find a topologically slice knot that is not smoothly slice, distinguishing topologically slice knots and smoothly slice knots has been extensively studied.

In 2012, in order to try to introduce some structure into the problem, Cochran, Harvey and Horn introduced a remarkable framework to study the set (actually a group) of topologically slice knots modulo smoothly slice knots, defining a geometrically inspired filtration, called the bipolar filtration. However a crucial question left unsettled was the non-triviality of the graded quotients. In joint work with Jae Choon Cha, we showed that the graded quotient of the bipolar filtration in fact has infinite rank, at each stage greater than one. In this talk, I will give a friendly, short introduction to knot theory in 3 and 4 dimensions, focussing on the differences between the smooth and topological categories, and I will briefly survey the recent progress on the bipolar filtration.

Contact anna.felikson@durham.ac.uk for more information


Informal HEP Journal club

Pure Maths Colloquium: The disparity between smooth and topologically slice knots

Presented by Min Hoon Kim, KIAS

2 October 2017 16:00 in CM221

Understanding the subtle difference between the topological and smooth categories is a central subject in 4-manifold topology. The local difference in the categories can be studied through knot theory. A knot in the 3-sphere is called smoothly slice (respectively, topologically slice) if it bounds a smoothly embedded (respectively, topologically embedded, locally flat) disc in the 4-ball.

After Casson used the celebrated results of Freedman and Donaldson on 4-dimensional manifolds to find a topologically slice knot that is not smoothly slice, distinguishing topologically slice knots and smoothly slice knots has been extensively studied.

In 2012, in order to try to introduce some structure into the problem, Cochran, Harvey and Horn introduced a remarkable framework to study the set (actually a group) of topologically slice knots modulo smoothly slice knots, defining a geometrically inspired filtration, called the bipolar filtration. However a crucial question left unsettled was the non-triviality of the graded quotients. In joint work with Jae Choon Cha, we showed that the graded quotient of the bipolar filtration in fact has infinite rank, at each stage greater than one. In this talk, I will give a friendly, short introduction to knot theory in 3 and 4 dimensions, focussing on the differences between the smooth and topological categories, and I will briefly survey the recent progress on the bipolar filtration.

Contact anna.felikson@durham.ac.uk for more information


Maths HEP Lunchtime Seminars

Pure Maths Colloquium: The disparity between smooth and topologically slice knots

Presented by Min Hoon Kim, KIAS

2 October 2017 16:00 in CM221

Understanding the subtle difference between the topological and smooth categories is a central subject in 4-manifold topology. The local difference in the categories can be studied through knot theory. A knot in the 3-sphere is called smoothly slice (respectively, topologically slice) if it bounds a smoothly embedded (respectively, topologically embedded, locally flat) disc in the 4-ball.

After Casson used the celebrated results of Freedman and Donaldson on 4-dimensional manifolds to find a topologically slice knot that is not smoothly slice, distinguishing topologically slice knots and smoothly slice knots has been extensively studied.

In 2012, in order to try to introduce some structure into the problem, Cochran, Harvey and Horn introduced a remarkable framework to study the set (actually a group) of topologically slice knots modulo smoothly slice knots, defining a geometrically inspired filtration, called the bipolar filtration. However a crucial question left unsettled was the non-triviality of the graded quotients. In joint work with Jae Choon Cha, we showed that the graded quotient of the bipolar filtration in fact has infinite rank, at each stage greater than one. In this talk, I will give a friendly, short introduction to knot theory in 3 and 4 dimensions, focussing on the differences between the smooth and topological categories, and I will briefly survey the recent progress on the bipolar filtration.

Contact anna.felikson@durham.ac.uk for more information


Pure Maths Colloquium

Pure Maths Colloquium: The disparity between smooth and topologically slice knots

Presented by Min Hoon Kim, KIAS

2 October 2017 16:00 in CM221

Understanding the subtle difference between the topological and smooth categories is a central subject in 4-manifold topology. The local difference in the categories can be studied through knot theory. A knot in the 3-sphere is called smoothly slice (respectively, topologically slice) if it bounds a smoothly embedded (respectively, topologically embedded, locally flat) disc in the 4-ball.

After Casson used the celebrated results of Freedman and Donaldson on 4-dimensional manifolds to find a topologically slice knot that is not smoothly slice, distinguishing topologically slice knots and smoothly slice knots has been extensively studied.

In 2012, in order to try to introduce some structure into the problem, Cochran, Harvey and Horn introduced a remarkable framework to study the set (actually a group) of topologically slice knots modulo smoothly slice knots, defining a geometrically inspired filtration, called the bipolar filtration. However a crucial question left unsettled was the non-triviality of the graded quotients. In joint work with Jae Choon Cha, we showed that the graded quotient of the bipolar filtration in fact has infinite rank, at each stage greater than one. In this talk, I will give a friendly, short introduction to knot theory in 3 and 4 dimensions, focussing on the differences between the smooth and topological categories, and I will briefly survey the recent progress on the bipolar filtration.

Contact anna.felikson@durham.ac.uk for more information


Statistics Seminars

Pure Maths Colloquium: The disparity between smooth and topologically slice knots

Presented by Min Hoon Kim, KIAS

2 October 2017 16:00 in CM221

Understanding the subtle difference between the topological and smooth categories is a central subject in 4-manifold topology. The local difference in the categories can be studied through knot theory. A knot in the 3-sphere is called smoothly slice (respectively, topologically slice) if it bounds a smoothly embedded (respectively, topologically embedded, locally flat) disc in the 4-ball.

After Casson used the celebrated results of Freedman and Donaldson on 4-dimensional manifolds to find a topologically slice knot that is not smoothly slice, distinguishing topologically slice knots and smoothly slice knots has been extensively studied.

In 2012, in order to try to introduce some structure into the problem, Cochran, Harvey and Horn introduced a remarkable framework to study the set (actually a group) of topologically slice knots modulo smoothly slice knots, defining a geometrically inspired filtration, called the bipolar filtration. However a crucial question left unsettled was the non-triviality of the graded quotients. In joint work with Jae Choon Cha, we showed that the graded quotient of the bipolar filtration in fact has infinite rank, at each stage greater than one. In this talk, I will give a friendly, short introduction to knot theory in 3 and 4 dimensions, focussing on the differences between the smooth and topological categories, and I will briefly survey the recent progress on the bipolar filtration.

Contact anna.felikson@durham.ac.uk for more information


Stats4Grads

Pure Maths Colloquium: The disparity between smooth and topologically slice knots

Presented by Min Hoon Kim, KIAS

2 October 2017 16:00 in CM221

Understanding the subtle difference between the topological and smooth categories is a central subject in 4-manifold topology. The local difference in the categories can be studied through knot theory. A knot in the 3-sphere is called smoothly slice (respectively, topologically slice) if it bounds a smoothly embedded (respectively, topologically embedded, locally flat) disc in the 4-ball.

After Casson used the celebrated results of Freedman and Donaldson on 4-dimensional manifolds to find a topologically slice knot that is not smoothly slice, distinguishing topologically slice knots and smoothly slice knots has been extensively studied.

In 2012, in order to try to introduce some structure into the problem, Cochran, Harvey and Horn introduced a remarkable framework to study the set (actually a group) of topologically slice knots modulo smoothly slice knots, defining a geometrically inspired filtration, called the bipolar filtration. However a crucial question left unsettled was the non-triviality of the graded quotients. In joint work with Jae Choon Cha, we showed that the graded quotient of the bipolar filtration in fact has infinite rank, at each stage greater than one. In this talk, I will give a friendly, short introduction to knot theory in 3 and 4 dimensions, focussing on the differences between the smooth and topological categories, and I will briefly survey the recent progress on the bipolar filtration.

Contact anna.felikson@durham.ac.uk for more information


Information about seminars for the current academic year. For information on previous years' seminars please see the seminar archives pages.