## Seminar information archive

Seminar information archive ～12/08｜Today's seminar 12/09 | Future seminars 12/10～

### 2013/04/17

#### Operator Algebra Seminars

16:30-18:00 Room #118 (Graduate School of Math. Sci. Bldg.)

Singularities, algebras, and the string landscape (ENGLISH)

**Tamar Friedmann**(Univ. Rochester)Singularities, algebras, and the string landscape (ENGLISH)

### 2013/04/16

#### Lie Groups and Representation Theory

16:30-18:30 Room #126 (Graduate School of Math. Sci. Bldg.)

Non-standard models for small representations of GL(n,R) (ENGLISH)

Degenerate principal series of symplectic groups (ENGLISH)

**Michael Pevzner**(Reims University) 16:30-17:30Non-standard models for small representations of GL(n,R) (ENGLISH)

[ Abstract ]

We shall present new models for some parabolically induced

unitary representations of the real general linear group which involve Weyl symbolic calculus and furnish very efficient tools in studying branching laws for such representations.

We shall present new models for some parabolically induced

unitary representations of the real general linear group which involve Weyl symbolic calculus and furnish very efficient tools in studying branching laws for such representations.

**Pierre Clare**(Penn. State University, USA) 17:30-18:30Degenerate principal series of symplectic groups (ENGLISH)

[ Abstract ]

We will discuss properties of representations of symplectic groups induced from maximal parabolic subgroups of Heisenberg type, including K-types formulas, expressions of intertwining operators and the study of their spectrum.

We will discuss properties of representations of symplectic groups induced from maximal parabolic subgroups of Heisenberg type, including K-types formulas, expressions of intertwining operators and the study of their spectrum.

### 2013/04/15

#### Lectures

15:00-16:30 Room #126 (Graduate School of Math. Sci. Bldg.)

Two-sided bounds for the Dirichlet heat kernel on inner uniform domains (ENGLISH)

**Janna Lierl**(University of Bonn)Two-sided bounds for the Dirichlet heat kernel on inner uniform domains (ENGLISH)

[ Abstract ]

I will present sharp two-sided bounds for the heat kernel in domains with Dirichlet boundary conditions. The domain is assumed to satisfy an inner uniformity condition. This includes any convex domain, the complement of any convex domain in Euclidean space, and the interior of the Koch snowflake.

The heat kernel estimates hold in the abstract setting of metric measure spaces equipped with a (possibly non-symmetric) Dirichlet form. The underlying space is assumed to satisfy a Poincare inequality and volume doubling.

The results apply, for example, to the Dirichlet heat kernel associated with a divergence form operator with bounded measurable coefficients and symmetric, uniformly elliptic second order part.

This is joint work with Laurent Saloff-Coste.

I will present sharp two-sided bounds for the heat kernel in domains with Dirichlet boundary conditions. The domain is assumed to satisfy an inner uniformity condition. This includes any convex domain, the complement of any convex domain in Euclidean space, and the interior of the Koch snowflake.

The heat kernel estimates hold in the abstract setting of metric measure spaces equipped with a (possibly non-symmetric) Dirichlet form. The underlying space is assumed to satisfy a Poincare inequality and volume doubling.

The results apply, for example, to the Dirichlet heat kernel associated with a divergence form operator with bounded measurable coefficients and symmetric, uniformly elliptic second order part.

This is joint work with Laurent Saloff-Coste.

#### Lectures

16:45-18:15 Room #126 (Graduate School of Math. Sci. Bldg.)

Persistence Probabilities (ENGLISH)

**Amir Dembo**(Stanford University)Persistence Probabilities (ENGLISH)

[ Abstract ]

Persistence probabilities concern how likely it is that a stochastic process has a long excursion above fixed level and of what are the relevant scenarios for this behavior. Power law decay is expected in many cases of physical significance and the issue is to determine its power exponent parameter. I will survey recent progress in this direction (jointly with Jian Ding, Fuchang Gao, and Sumit Mukherjee), dealing with random algebraic polynomials of independent coefficients, iterated partial sums and other auto-regressive sequences, and with the solution to heat equation initiated by white noise.

Persistence probabilities concern how likely it is that a stochastic process has a long excursion above fixed level and of what are the relevant scenarios for this behavior. Power law decay is expected in many cases of physical significance and the issue is to determine its power exponent parameter. I will survey recent progress in this direction (jointly with Jian Ding, Fuchang Gao, and Sumit Mukherjee), dealing with random algebraic polynomials of independent coefficients, iterated partial sums and other auto-regressive sequences, and with the solution to heat equation initiated by white noise.

#### Seminar on Geometric Complex Analysis

10:30-12:00 Room #126 (Graduate School of Math. Sci. Bldg.)

On defining functions for unbounded pseudoconvex domains (ENGLISH)

**Nikolay Shcherbina**(University of Wuppertal)On defining functions for unbounded pseudoconvex domains (ENGLISH)

[ Abstract ]

We show that every strictly pseudoconvex domain $\Omega$ with smooth boundary in a complex manifold $M$ admits a global defining function, i.e. a smooth plurisubharmonic function $\varphi \colon U \to \mathbf{R}$ defined on an open neighbourhood $U \subset M$ of $\Omega$ such that $\Omega =\{ \varphi < 0 \}$, $d\varphi \not= 0$ on $b\Omega$ and $\varphi$ is strictly plurisubharmonic near $b\Omega$. We then introduce the notion of the kernel $K(\Omega)$ of an arbitrary domain $\Omega \subset M$ as the set of all points where every smooth and bounded from above plurisubharmonic function on $\Omega$ fails to be strictly plurisubharmonic. If $\Omega$ is not relatively compact in $M$, then in general $K(\Omega)$ is nonempty, even in the case when $M$ is Stein. It is shown that every strictly pseudoconvex domain $\Omega \subset M$ with smooth boundary admits a global defining function that is strictly plurisubharmonic precisely in the complement of $K(\Omega)$. We then investigate properties of the kernel. Among other results we prove 1-pseudoconcavity of the kernel, we show that in general the kernel does not possess any analytic structure, and we investigate Liouville type properties of the kernel.

We show that every strictly pseudoconvex domain $\Omega$ with smooth boundary in a complex manifold $M$ admits a global defining function, i.e. a smooth plurisubharmonic function $\varphi \colon U \to \mathbf{R}$ defined on an open neighbourhood $U \subset M$ of $\Omega$ such that $\Omega =\{ \varphi < 0 \}$, $d\varphi \not= 0$ on $b\Omega$ and $\varphi$ is strictly plurisubharmonic near $b\Omega$. We then introduce the notion of the kernel $K(\Omega)$ of an arbitrary domain $\Omega \subset M$ as the set of all points where every smooth and bounded from above plurisubharmonic function on $\Omega$ fails to be strictly plurisubharmonic. If $\Omega$ is not relatively compact in $M$, then in general $K(\Omega)$ is nonempty, even in the case when $M$ is Stein. It is shown that every strictly pseudoconvex domain $\Omega \subset M$ with smooth boundary admits a global defining function that is strictly plurisubharmonic precisely in the complement of $K(\Omega)$. We then investigate properties of the kernel. Among other results we prove 1-pseudoconcavity of the kernel, we show that in general the kernel does not possess any analytic structure, and we investigate Liouville type properties of the kernel.

### 2013/04/11

#### Geometry Colloquium

10:00-11:30 Room #122 (Graduate School of Math. Sci. Bldg.)

Critical metrics on connected sums of Einstein four-manifolds (ENGLISH)

**Jeff Viaclovsky**(University of Wisconsin)Critical metrics on connected sums of Einstein four-manifolds (ENGLISH)

[ Abstract ]

I will discuss a gluing procedure designed to obtain critical metrics of quadratic Riemannian functionals on connected sums of certain Einstein four-manifolds. Start with two Einstein four-manifolds of positive scalar curvature which are "rigid". Using the Green's function for the conformal Laplacian, convert one of these into an asymptotically flat (AF) scalar-flat metric. A "naive" approximate critical metric is obtained by identifying the boundary of a large ball in the AF metric with the boundary of a small ball in the other compact Einstein metric, using cutoff functions to glue together the AF metric with a suitably scaled compact metric in order to obtain a smooth metric on the connected sum. It turns out that this naive approximate metric is too rough, and must be refined in order to compute the leading term of the Kuranishi map. The main application is an existence result using two well-known Einstein manifolds as building blocks: the Fubini-Study metric on $¥mathbb{CP}^2$ and the product metric on $S^2 ¥times S^2$. Using these factors in various gluing configurations, a zero of the Kuranishi map is then found for a specific quadratic Riemannian functional on certain connected sums. The exact functional depends on the geometry of the factors, and also on the mass of the AF metric. Using certain quotients of $S^2 ¥times S^2$ as one of the gluing factors, several non-simply connected examples are also obtained. This is joint work with Matt Gursky.

I will discuss a gluing procedure designed to obtain critical metrics of quadratic Riemannian functionals on connected sums of certain Einstein four-manifolds. Start with two Einstein four-manifolds of positive scalar curvature which are "rigid". Using the Green's function for the conformal Laplacian, convert one of these into an asymptotically flat (AF) scalar-flat metric. A "naive" approximate critical metric is obtained by identifying the boundary of a large ball in the AF metric with the boundary of a small ball in the other compact Einstein metric, using cutoff functions to glue together the AF metric with a suitably scaled compact metric in order to obtain a smooth metric on the connected sum. It turns out that this naive approximate metric is too rough, and must be refined in order to compute the leading term of the Kuranishi map. The main application is an existence result using two well-known Einstein manifolds as building blocks: the Fubini-Study metric on $¥mathbb{CP}^2$ and the product metric on $S^2 ¥times S^2$. Using these factors in various gluing configurations, a zero of the Kuranishi map is then found for a specific quadratic Riemannian functional on certain connected sums. The exact functional depends on the geometry of the factors, and also on the mass of the AF metric. Using certain quotients of $S^2 ¥times S^2$ as one of the gluing factors, several non-simply connected examples are also obtained. This is joint work with Matt Gursky.

### 2013/04/10

#### Operator Algebra Seminars

16:30-18:00 Room #118 (Graduate School of Math. Sci. Bldg.)

On nuclearity of $C^*$-algebras associated with Fell bundles over \\'etale groupoids (ENGLISH)

**Takuya Takeishi**(Univ. Tokyo)On nuclearity of $C^*$-algebras associated with Fell bundles over \\'etale groupoids (ENGLISH)

#### Number Theory Seminar

17:30-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)

Motivic structure on higher homotopy of non-nilpotent spaces (ENGLISH)

**Deepam Patel**(University of Amsterdam)Motivic structure on higher homotopy of non-nilpotent spaces (ENGLISH)

[ Abstract ]

In his fundamental paper on the projective line minus three points, Deligne constructed certain extensions of mixed Tate motives arising from the fundamental group of the projective line minus three points. Since then, motivic structures on homotopy groups have been studied by many authors. In this talk, we will construct a motivic structure on the (nilpotent completion of) n-th homotopy group of P^{n} minus n+2 hyperplanes in general position.

In his fundamental paper on the projective line minus three points, Deligne constructed certain extensions of mixed Tate motives arising from the fundamental group of the projective line minus three points. Since then, motivic structures on homotopy groups have been studied by many authors. In this talk, we will construct a motivic structure on the (nilpotent completion of) n-th homotopy group of P^{n} minus n+2 hyperplanes in general position.

### 2013/04/09

#### Tuesday Seminar on Topology

16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)

Colored HOMFLY Homology and Super-A-polynomial (JAPANESE)

**Hiroyuki Fuji**(The University of Tokyo)Colored HOMFLY Homology and Super-A-polynomial (JAPANESE)

[ Abstract ]

This talk is based on works in collaboration with S. Gukov, M. Stosic,

and P. Sulkowski. We study the colored HOMFLY homology for knots and

its asymptotic behavior. In recent years, the categorification of the

colored HOMFLY polynomial is proposed in term of homological

discussions via spectral sequence and physical discussions via refined

topological string, and these proposals give the same answer

miraculously. In this talk, we consider the asymptotic behavior of the

colored HOMFLY homology \\`a la the generalized volume conjecture, and

discuss the quantum structure of the colored HOMFLY homology for the

complete symmetric representations via the generalized A-polynomial

which we call “super-A-polynomial”.

This talk is based on works in collaboration with S. Gukov, M. Stosic,

and P. Sulkowski. We study the colored HOMFLY homology for knots and

its asymptotic behavior. In recent years, the categorification of the

colored HOMFLY polynomial is proposed in term of homological

discussions via spectral sequence and physical discussions via refined

topological string, and these proposals give the same answer

miraculously. In this talk, we consider the asymptotic behavior of the

colored HOMFLY homology \\`a la the generalized volume conjecture, and

discuss the quantum structure of the colored HOMFLY homology for the

complete symmetric representations via the generalized A-polynomial

which we call “super-A-polynomial”.

#### Lie Groups and Representation Theory

16:30-18:00 Room #126 (Graduate School of Math. Sci. Bldg.)

A characterization of non-tube type Hermitian symmetric spaces by visible actions

(JAPANESE)

**Atsumu Sasaki**(Tokai University)A characterization of non-tube type Hermitian symmetric spaces by visible actions

(JAPANESE)

[ Abstract ]

We consider a non-symmetric complex Stein manifold D

which is realized as a line bundle over the complexification of a non-compact irreducible Hermitian symmetric space G/K.

In this talk, we will explain that the compact group action on D is strongly visible in the sense of Toshiyuki Kobayashi if and only if G/K is of non-tube type.

In particular, we focus on our construction of slice which meets every orbit in D from the viewpoint of group theory, namely,

we find an A-part of a generalized Cartan decomposition for homogeneous space D.

We note that our choice of A-part is an abelian.

We consider a non-symmetric complex Stein manifold D

which is realized as a line bundle over the complexification of a non-compact irreducible Hermitian symmetric space G/K.

In this talk, we will explain that the compact group action on D is strongly visible in the sense of Toshiyuki Kobayashi if and only if G/K is of non-tube type.

In particular, we focus on our construction of slice which meets every orbit in D from the viewpoint of group theory, namely,

we find an A-part of a generalized Cartan decomposition for homogeneous space D.

We note that our choice of A-part is an abelian.

### 2013/04/08

#### Seminar on Geometric Complex Analysis

10:30-12:00 Room #126 (Graduate School of Math. Sci. Bldg.)

K\\"ahler-Einstein metrics and K stability (JAPANESE)

**Akito Futaki**(University of Tokyo)K\\"ahler-Einstein metrics and K stability (JAPANESE)

[ Abstract ]

I will describe an outline of the proof of the equivalence between the existence of K\\"ahler-Einstein metrics and K-stablity after Chen-Donaldson-Sun and Tian.

I will describe an outline of the proof of the equivalence between the existence of K\\"ahler-Einstein metrics and K-stablity after Chen-Donaldson-Sun and Tian.

### 2013/04/02

#### Lie Groups and Representation Theory

16:30-18:00 Room #126 (Graduate School of Math. Sci. Bldg.)

Discrete branching laws of Zuckerman's derived functor modules (JAPANESE)

**Yoshiki Oshima**(Kavli IPMU, the University of Tokyo)Discrete branching laws of Zuckerman's derived functor modules (JAPANESE)

[ Abstract ]

We consider the restriction of Zuckerman's derived functor modules with respect to symmetric pairs of real reductive groups. When they are discretely decomposable, explicit formulas for the branching laws are obtained by using a realization as D-module on the flag variety and the generalized BGG resolution. In this talk we would like to illustrate how to derive the formulas with a few examples.

We consider the restriction of Zuckerman's derived functor modules with respect to symmetric pairs of real reductive groups. When they are discretely decomposable, explicit formulas for the branching laws are obtained by using a realization as D-module on the flag variety and the generalized BGG resolution. In this talk we would like to illustrate how to derive the formulas with a few examples.

### 2013/03/30

#### Infinite Analysis Seminar Tokyo

13:30-15:30 Room #002 (Graduate School of Math. Sci. Bldg.)

On the extended algebra of type sl_2 at positive rational level (ENGLISH)

**Simon Wood**(Kavli IPMU)On the extended algebra of type sl_2 at positive rational level (ENGLISH)

[ Abstract ]

I will be presenting my recent work with Akihiro Tsuchiya

(arXiv:1302.6435).

I will explain how to construct a certain VOA called the "extended

algebra of type sl_2 at positive rational level"

as a subVOA of a lattice VOA, by means of screening operators. I will

then show that this VOA carries a kind of exterior sl_2 action and then

show how one can compute the structure Zhu's algebra and the Poisson

algebra as well as classify all simple modules by using the screening

operators and the sl_2 action. Important concepts such as screening

operators or Zhu's algebra and the Poisson algebra of a VOA will be

reviewed in the talk.

I will be presenting my recent work with Akihiro Tsuchiya

(arXiv:1302.6435).

I will explain how to construct a certain VOA called the "extended

algebra of type sl_2 at positive rational level"

as a subVOA of a lattice VOA, by means of screening operators. I will

then show that this VOA carries a kind of exterior sl_2 action and then

show how one can compute the structure Zhu's algebra and the Poisson

algebra as well as classify all simple modules by using the screening

operators and the sl_2 action. Important concepts such as screening

operators or Zhu's algebra and the Poisson algebra of a VOA will be

reviewed in the talk.

### 2013/03/19

#### Tuesday Seminar on Topology

16:30-18:00 Room #002 (Graduate School of Math. Sci. Bldg.)

Open book foliation and application to contact topology (ENGLISH)

**Keiko Kawamuro**(University of Iowa)Open book foliation and application to contact topology (ENGLISH)

[ Abstract ]

Open book foliation is a generalization of Birman and Menasco's braid foliation. Any 3-manifold admits open book decompositions. Open book foliation is a singular foliation on an embedded surface, and is define by the intersection of a surface and the pages of the open book decomposition. By Giroux's identification of open books and contact structures one can use open book foliation method to study contact structures. In this talk I define the open book foliation and show some applications to contact topology. This is joint work with Tetsuya Ito (University of British Columbia).

Open book foliation is a generalization of Birman and Menasco's braid foliation. Any 3-manifold admits open book decompositions. Open book foliation is a singular foliation on an embedded surface, and is define by the intersection of a surface and the pages of the open book decomposition. By Giroux's identification of open books and contact structures one can use open book foliation method to study contact structures. In this talk I define the open book foliation and show some applications to contact topology. This is joint work with Tetsuya Ito (University of British Columbia).

### 2013/03/18

#### Operator Algebra Seminars

16:00-17:30 Room #118 (Graduate School of Math. Sci. Bldg.)

Ultraproducts of von Neumann algebras (JAPANESE)

**Hiroshi Ando**(IHES)Ultraproducts of von Neumann algebras (JAPANESE)

#### Colloquium

15:00-17:30 Room #050 (Graduate School of Math. Sci. Bldg.)

Value distribution theory and analytic function theory in several variables (JAPANESE)

My fifty years of differential equations (JAPANESE)

**NOGUCHI, Junjiro**(University of Tokyo) 15:00-16:00Value distribution theory and analytic function theory in several variables (JAPANESE)

**OSHIMA, Toshio**(University of Tokyo) 16:30-17:30My fifty years of differential equations (JAPANESE)

### 2013/03/15

#### Operator Algebra Seminars

15:45-18:00 Room #118 (Graduate School of Math. Sci. Bldg.)

Infinitesimal 2-Yang-Baxter operators from a categorification

of the Knizhnik-Zamolodchikov connection (ENGLISH)

Twisted tensor product of $C^*$-algebras (ENGLISH)

**Lucio Cirio**(Univ. M\"unster) 15:45-16:45Infinitesimal 2-Yang-Baxter operators from a categorification

of the Knizhnik-Zamolodchikov connection (ENGLISH)

**Sutanu Roy**(Univ. G\"ottingen) 17:00-18:00Twisted tensor product of $C^*$-algebras (ENGLISH)

#### Numerical Analysis Seminar

10:00-12:15 Room #056 (Graduate School of Math. Sci. Bldg.)

Complex flow at the boundaries of branched models: numerical aspects (ENGLISH)

[ Reference URL ]

http://www.infsup.jp/utnas/

**Irene Vignon-Clementel**(INRIA Paris Rocquencourt )Complex flow at the boundaries of branched models: numerical aspects (ENGLISH)

[ Reference URL ]

http://www.infsup.jp/utnas/

#### Operator Algebra Seminars

14:30-15:30 Room #118 (Graduate School of Math. Sci. Bldg.)

The connected component of a compact quantum group (ENGLISH)

**Stefano Rossi**(Univ. Roma II)The connected component of a compact quantum group (ENGLISH)

#### Operator Algebra Seminars

13:15-14:15 Room #118 (Graduate School of Math. Sci. Bldg.)

Two Amir-Cambern type theorems for $C^*$-algebras (ENGLISH)

**Jean Roydor**(Univ. Bordeaux)Two Amir-Cambern type theorems for $C^*$-algebras (ENGLISH)

#### PDE Real Analysis Seminar

10:30-11:30 Room #128 (Graduate School of Math. Sci. Bldg.)

Geometric rigidity for incompatible fields and an application to strain-gradient plasticity (ENGLISH)

**Caterina Zeppieri**(Universität Münster)Geometric rigidity for incompatible fields and an application to strain-gradient plasticity (ENGLISH)

[ Abstract ]

Motivated by the study of nonlinear plane elasticity in presence of edge dislocations, in this talk we show that in dimension two the Friesecke, James, and Müller Rigidity Estimate holds true also for matrix-fields with nonzero curl, modulo an error depending on the total mass of the curl.

The above generalised rigidity is then used to derive a strain-gradient model for plasticity from semi-discrete nonlinear dislocation energies by Gamma-convergence.

The above results are obtained in collaboration with S. Müller (University of Bonn, Germany) and L. Scardia (University of Glasgow, UK).

Motivated by the study of nonlinear plane elasticity in presence of edge dislocations, in this talk we show that in dimension two the Friesecke, James, and Müller Rigidity Estimate holds true also for matrix-fields with nonzero curl, modulo an error depending on the total mass of the curl.

The above generalised rigidity is then used to derive a strain-gradient model for plasticity from semi-discrete nonlinear dislocation energies by Gamma-convergence.

The above results are obtained in collaboration with S. Müller (University of Bonn, Germany) and L. Scardia (University of Glasgow, UK).

### 2013/03/11

#### Operator Algebra Seminars

09:45-12:00 Room #123 (Graduate School of Math. Sci. Bldg.)

Traces and Ultrapowers (ENGLISH)

Constructing subfactors with jellyfish (ENGLISH)

**Tristan Bice**(York Univ.) 09:45-10:45Traces and Ultrapowers (ENGLISH)

**David Penneys**(Univ. Toronto) 11:00-12:00Constructing subfactors with jellyfish (ENGLISH)

#### Operator Algebra Seminars

13:30-18:15 Room #123 (Graduate School of Math. Sci. Bldg.)

Classification and the Toms-Winter Conjecture (ENGLISH)

Free probability and planar algebras (ENGLISH)

Kirchberg $X$-algebras with real rank zero and intermediate cancellation (ENGLISH)

Classifying $C^*$-algebras up to W-stability (ENGLISH)

**Danny Hey**(Univ. Toronto) 13:30-14:30Classification and the Toms-Winter Conjecture (ENGLISH)

**Stephen Curran**(UCLA) 14:45-15:45Free probability and planar algebras (ENGLISH)

**Rasmus Bentmann**(Univ. Copenhagen) 16:00-17:00Kirchberg $X$-algebras with real rank zero and intermediate cancellation (ENGLISH)

**Luis Santiago-Moreno**(Univ. Oregon) 17:15-18:15Classifying $C^*$-algebras up to W-stability (ENGLISH)

#### GCOE Seminars

14:45-15:45 Room #123 (Graduate School of Math. Sci. Bldg.)

Free probability and planar algebras (ENGLISH)

[ Reference URL ]

https://www.ms.u-tokyo.ac.jp/~yasuyuki/mini2013-4.htm

**Stephen Curran**(UCLA)Free probability and planar algebras (ENGLISH)

[ Reference URL ]

https://www.ms.u-tokyo.ac.jp/~yasuyuki/mini2013-4.htm

### 2013/03/08

#### FMSP Lectures

10:30-12:00 Room #056 (Graduate School of Math. Sci. Bldg.)

Knots, algorithms and linear programming: the quest to solve unknot recognition in polynomial time (ENGLISH)

**Benjamin Burton**(The University of Queensland, Australia)Knots, algorithms and linear programming: the quest to solve unknot recognition in polynomial time (ENGLISH)

[ Abstract ]

In this talk we explore new approaches to the old and difficult computational problem of unknot recognition. Although the best known algorithms for this problem run in exponential time, there is increasing evidence that a polynomial time solution might be possible. We outline several promising approaches, in which computational geometry, linear programming and greedy algorithms all play starring roles. We finish with a new algorithm that combines techniques from topology and combinatorial optimisation, which is the first to exhibit "real world" polynomial time behaviour: although it is still exponential time in theory, exhaustive experimentation shows that this algorithm can solve unknot recognition for "practical" inputs by running just a linear number of linear programs.

This is joint work with Melih Ozlen.

In this talk we explore new approaches to the old and difficult computational problem of unknot recognition. Although the best known algorithms for this problem run in exponential time, there is increasing evidence that a polynomial time solution might be possible. We outline several promising approaches, in which computational geometry, linear programming and greedy algorithms all play starring roles. We finish with a new algorithm that combines techniques from topology and combinatorial optimisation, which is the first to exhibit "real world" polynomial time behaviour: although it is still exponential time in theory, exhaustive experimentation shows that this algorithm can solve unknot recognition for "practical" inputs by running just a linear number of linear programs.

This is joint work with Melih Ozlen.

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