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Future seminars
Seminar information archive ～12/05｜Today's seminar 12/06 | Future seminars 12/07～
2024/12/09
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Yoshiaki Suzuki (Niigata Univ.)
The spectrum of the Folland-Stein operator on some Heisenberg Bieberbach manifolds (Japanese)
https://forms.gle/gTP8qNZwPyQyxjTj8
Yoshiaki Suzuki (Niigata Univ.)
The spectrum of the Folland-Stein operator on some Heisenberg Bieberbach manifolds (Japanese)
[ Abstract ]
.
[ Reference URL ].
https://forms.gle/gTP8qNZwPyQyxjTj8
Tokyo Probability Seminar
16:00-17:30 Room #126 (Graduate School of Math. Sci. Bldg.)
We are having teatime from 15:15 in the common room on the second floor. Please join us.
Hayate Suda (Institute of Science Tokyo)
Scaling limits of a tagged soliton in the randomized box-ball system
We are having teatime from 15:15 in the common room on the second floor. Please join us.
Hayate Suda (Institute of Science Tokyo)
Scaling limits of a tagged soliton in the randomized box-ball system
[ Abstract ]
The box-ball system (BBS) is a cellular automaton that exhibits the solitonic behavior. In recent years, with the rapid progress in the study of the hydrodynamics of integrable systems, there has been a growing interest in BBS with random initial distribution. In this talk, we consider the scaling limits for a tagged soliton in the BBS starting from certain stationary distribution. This talk is based on a joint work with Stefano Olla and Makiko Sasada.
The box-ball system (BBS) is a cellular automaton that exhibits the solitonic behavior. In recent years, with the rapid progress in the study of the hydrodynamics of integrable systems, there has been a growing interest in BBS with random initial distribution. In this talk, we consider the scaling limits for a tagged soliton in the BBS starting from certain stationary distribution. This talk is based on a joint work with Stefano Olla and Makiko Sasada.
2024/12/10
Tuesday Seminar on Topology
17:00-18:30 Room #ハイブリッド開催/056 (Graduate School of Math. Sci. Bldg.)
Pre-registration required. See our seminar webpage.
Shun Wakatsuki (Nagoya University)
Computation of the magnitude homology as a derived functor (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Shun Wakatsuki (Nagoya University)
Computation of the magnitude homology as a derived functor (JAPANESE)
[ Abstract ]
Asao-Ivanov showed that the magnitude homology of a finite metric space is isomorphic to the derived functor Tor over some ring. In this talk, I will explain an application of the theory of minimal projective resolution to this derived functor. Especially in the case of a geodetic graph, torsion-freeness and a criterion for diagonality of the magnitude homology are established. Moreover, I will give computational examples including cyclic graphs. This is a joint work with Yasuhiko Asao.
[ Reference URL ]Asao-Ivanov showed that the magnitude homology of a finite metric space is isomorphic to the derived functor Tor over some ring. In this talk, I will explain an application of the theory of minimal projective resolution to this derived functor. Especially in the case of a geodetic graph, torsion-freeness and a criterion for diagonality of the magnitude homology are established. Moreover, I will give computational examples including cyclic graphs. This is a joint work with Yasuhiko Asao.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Operator Algebra Seminars
15:00-16:30 Room #002 (Graduate School of Math. Sci. Bldg.)
Yoh Tanimoto (Univ. Rome, "Tor Vergata")
Introduction to Lean theorem prover
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Yoh Tanimoto (Univ. Rome, "Tor Vergata")
Introduction to Lean theorem prover
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Operator Algebra Seminars
16:45-18:15 Room #002 (Graduate School of Math. Sci. Bldg.)
Maria Stella Adamo (FAU Erlangen-Nürnberg)
Osterwalder-Schrader axioms for unitary full VOAs
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Maria Stella Adamo (FAU Erlangen-Nürnberg)
Osterwalder-Schrader axioms for unitary full VOAs
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
2024/12/11
Number Theory Seminar
17:00-18:00 Room #117 (Graduate School of Math. Sci. Bldg.)
Ryosuke Ooe (University of Tokyo)
The characteristic cycle of an l-adic sheaf on a smooth variety (Japanese)
Ryosuke Ooe (University of Tokyo)
The characteristic cycle of an l-adic sheaf on a smooth variety (Japanese)
[ Abstract ]
The characteristic cycle of an l-adic sheaf on a smooth variety over a perfect field is defined by Saito as a cycle on the cotangent bundle and the intersection with the zero section computes the Euler number. On the other hand, the characteristic cycle of an l-adic sheaf on a regular scheme in mixed characteristic is not yet defined. In this talk, I define the F-characteristic cycle of a rank one sheaf on an arithmetic surface whose intersection with the zero section computes the Swan conductor of the cohomology of the generic fiber. The definition is based on the computation of the characteristic cycle in equal characteristic by Yatagawa. I explain the rationality and the integrality of the characteristic form of an abelian character, which are necessary for the definition of the F-characteristic cycle.
The characteristic cycle of an l-adic sheaf on a smooth variety over a perfect field is defined by Saito as a cycle on the cotangent bundle and the intersection with the zero section computes the Euler number. On the other hand, the characteristic cycle of an l-adic sheaf on a regular scheme in mixed characteristic is not yet defined. In this talk, I define the F-characteristic cycle of a rank one sheaf on an arithmetic surface whose intersection with the zero section computes the Swan conductor of the cohomology of the generic fiber. The definition is based on the computation of the characteristic cycle in equal characteristic by Yatagawa. I explain the rationality and the integrality of the characteristic form of an abelian character, which are necessary for the definition of the F-characteristic cycle.
2024/12/12
Algebraic Geometry Seminar
13:30-15:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Chenyang Xu (Princeton University)
Irreducible symplectic varieties with a large second Betti number
Chenyang Xu (Princeton University)
Irreducible symplectic varieties with a large second Betti number
[ Abstract ]
(joint with Yuchen Liu, Zhiyu Liu) We show that the Lagrangian fibration constructed by Iiiev-Manivel using intermediate Jacobians of cubic fivefolds containing a fixed cubic fourfold, admits a compactification as a terminal Q-factorial irreducible symplectic varieties. As far as I know, besides OG10, this is the second family of irreducible symplectic varieties with the second Betti number at least 24.
(joint with Yuchen Liu, Zhiyu Liu) We show that the Lagrangian fibration constructed by Iiiev-Manivel using intermediate Jacobians of cubic fivefolds containing a fixed cubic fourfold, admits a compactification as a terminal Q-factorial irreducible symplectic varieties. As far as I know, besides OG10, this is the second family of irreducible symplectic varieties with the second Betti number at least 24.
2024/12/16
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Laurent Stolovitch (Universite Cote d'Azur)
CR singularities and dynamical systems (English)
https://forms.gle/gTP8qNZwPyQyxjTj8
Laurent Stolovitch (Universite Cote d'Azur)
CR singularities and dynamical systems (English)
[ Abstract ]
In this talk, we'll survey some recent results done since the seminal work of Moser and Webster about smooth real analytic surfaces in $C^2$ which are totally real everywhere but at a point where the tangent space is a complex line. Such a point is called a singularity of the Cauchy-Riemann structure. We are interested in the holomorphic classification of these surface near the singularity. It happens that there is a deep connection with holomorphic classification of some holomorphic dynamical systems near a fixed point so that new results for the later provide new result for the former.
[ Reference URL ]In this talk, we'll survey some recent results done since the seminal work of Moser and Webster about smooth real analytic surfaces in $C^2$ which are totally real everywhere but at a point where the tangent space is a complex line. Such a point is called a singularity of the Cauchy-Riemann structure. We are interested in the holomorphic classification of these surface near the singularity. It happens that there is a deep connection with holomorphic classification of some holomorphic dynamical systems near a fixed point so that new results for the later provide new result for the former.
https://forms.gle/gTP8qNZwPyQyxjTj8
2024/12/17
Tuesday Seminar on Topology
17:00-18:30 Room #hybrid/056 (Graduate School of Math. Sci. Bldg.)
Pre-registration required. See our seminar webpage.
Emmanuel Graff (The University of Tokyo)
Is there torsion in the homotopy braid group? (ENGLISH)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Emmanuel Graff (The University of Tokyo)
Is there torsion in the homotopy braid group? (ENGLISH)
[ Abstract ]
In the 'Kourovka notebook,' V. Lin questions the existence of a non-trivial epimorphism from the braid group onto a non-abelian torsion-free group. The homotopy braid group, studied by Goldsmith in 1974, naturally appears as a potential candidate. In 2001, Humphries showed that this homotopy braid group is torsion-free for less than six strands. In this presentation, we will see a new approach based on the broader concept of welded braids, along with algebraic techniques, to determine whether the homotopy braid group provides a complete answer to Lin’s question.
[ Reference URL ]In the 'Kourovka notebook,' V. Lin questions the existence of a non-trivial epimorphism from the braid group onto a non-abelian torsion-free group. The homotopy braid group, studied by Goldsmith in 1974, naturally appears as a potential candidate. In 2001, Humphries showed that this homotopy braid group is torsion-free for less than six strands. In this presentation, we will see a new approach based on the broader concept of welded braids, along with algebraic techniques, to determine whether the homotopy braid group provides a complete answer to Lin’s question.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Operator Algebra Seminars
16:45-18:15 Room #122 (Graduate School of Math. Sci. Bldg.)
Makoto Yamashita (Univ. Oslo)
TBA
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Makoto Yamashita (Univ. Oslo)
TBA
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
2024/12/18
Seminar on Mathematics for various disciplines
10:30-11:30 Room #122 (Graduate School of Math. Sci. Bldg.)
This seminar is held on Wednesday in Room 122 and online.
Amy Novick-Cohen (Technion - Israel Institute of Technology)
Diffusion: Some new results and approaches (English)
https://u-tokyo-ac-jp.zoom.us/j/83306203126?pwd=b92LqeuB5sLUkN2LKu7Mp8SQmoSbAU.1
This seminar is held on Wednesday in Room 122 and online.
Amy Novick-Cohen (Technion - Israel Institute of Technology)
Diffusion: Some new results and approaches (English)
[ Abstract ]
We first briefly review a variety of geometries where surface diffusion is meaningful in the context of the stability of thin solid state films. Afterwards, we discuss joint work with E.A. Carlen & L. Peres Hari (2024), which focuses on rigorously establishing a connection between surface diffusion and the deep quench obstacle problem with a suitable degenerate mobility. Our study begins by rigorously establishing a connection between certain steady states of the respective systems, and then outlines a method for connecting the respective evolutions via minimizing motion descriptions.
Please join the Zoom meeting at the [Reference URL] below.
Meeting ID: 833 0620 3126
Passcode: 223203
[ Reference URL ]We first briefly review a variety of geometries where surface diffusion is meaningful in the context of the stability of thin solid state films. Afterwards, we discuss joint work with E.A. Carlen & L. Peres Hari (2024), which focuses on rigorously establishing a connection between surface diffusion and the deep quench obstacle problem with a suitable degenerate mobility. Our study begins by rigorously establishing a connection between certain steady states of the respective systems, and then outlines a method for connecting the respective evolutions via minimizing motion descriptions.
Please join the Zoom meeting at the [Reference URL] below.
Meeting ID: 833 0620 3126
Passcode: 223203
https://u-tokyo-ac-jp.zoom.us/j/83306203126?pwd=b92LqeuB5sLUkN2LKu7Mp8SQmoSbAU.1
2024/12/19
Infinite Analysis Seminar Tokyo
14:00-15:30 Room #002 (Graduate School of Math. Sci. Bldg.)
Omar Kidwai (The Chinese University of Hong Kong)
Quadratic differentials and Donaldson-Thomas invariants (English)
Omar Kidwai (The Chinese University of Hong Kong)
Quadratic differentials and Donaldson-Thomas invariants (English)
[ Abstract ]
We recall the relation between quadratic differentials and spaces of stability conditions due to Bridgeland-Smith. We describe the calculation of (refined) Donaldson-Thomas invariants for stability conditions on a certain class of 3-Calabi-Yau triangulated categories studied by Christ-Haiden-Qiu. This category is slightly different from the usual one discussed by Bridgeland and Smith, which in particular allows us to recover a nonzero invariant in the case where the quadratic differential has a second-order pole, in agreement with predictions from the physics literature. Based on joint work with N. Williams.
We recall the relation between quadratic differentials and spaces of stability conditions due to Bridgeland-Smith. We describe the calculation of (refined) Donaldson-Thomas invariants for stability conditions on a certain class of 3-Calabi-Yau triangulated categories studied by Christ-Haiden-Qiu. This category is slightly different from the usual one discussed by Bridgeland and Smith, which in particular allows us to recover a nonzero invariant in the case where the quadratic differential has a second-order pole, in agreement with predictions from the physics literature. Based on joint work with N. Williams.
2024/12/20
Colloquium
15:30-16:30 Room #大講義室 (Graduate School of Math. Sci. Bldg.)
Hideo Kozono (Waseda University / Tohoku University)
Helmholtz-Weyl decomposition and its application to the magnetohydrodynamic equations (日本語)
https://forms.gle/QNj3fohg3ZRMD8RHA
Hideo Kozono (Waseda University / Tohoku University)
Helmholtz-Weyl decomposition and its application to the magnetohydrodynamic equations (日本語)
[ Abstract ]
We consider the Helmoltz-Weyl decomosition for $L^r$-vector fields in 3D bounded domains with the smooth boundary. The de Rham-Hodge-Kodaira decomposition of the $p$-form on compact Riemannian manifolds are well-known. However, in the general $L^r$-setting, such a decomposition has been relatively recently studied by
Fujiwara-Morimoto. In this talk, we deal with the 3D case and characterize two kinds of the space of harmonic vector fields in terms of the boundary condition where the vector fields are tangential or perpendicular to the boundary. Then it is clarified that the $L^r$-vector field is decomposed as a direct sum into harmonic, rotational and gradient parts. In particular, we bring the structure of the space with vector potentials into focus. As an application, we prove the asymptotic stability of the equilibrium to the magnetoydrodynamic equations associated with the harmonic vector field in the domain with the non-zero second Betti number. This is based on the joint work with Prof. Senjo Shimizu(Kyoto Univ.) and Prof. Taku Yanagisawa(Nara Women Univ.).
[ Reference URL ]We consider the Helmoltz-Weyl decomosition for $L^r$-vector fields in 3D bounded domains with the smooth boundary. The de Rham-Hodge-Kodaira decomposition of the $p$-form on compact Riemannian manifolds are well-known. However, in the general $L^r$-setting, such a decomposition has been relatively recently studied by
Fujiwara-Morimoto. In this talk, we deal with the 3D case and characterize two kinds of the space of harmonic vector fields in terms of the boundary condition where the vector fields are tangential or perpendicular to the boundary. Then it is clarified that the $L^r$-vector field is decomposed as a direct sum into harmonic, rotational and gradient parts. In particular, we bring the structure of the space with vector potentials into focus. As an application, we prove the asymptotic stability of the equilibrium to the magnetoydrodynamic equations associated with the harmonic vector field in the domain with the non-zero second Betti number. This is based on the joint work with Prof. Senjo Shimizu(Kyoto Univ.) and Prof. Taku Yanagisawa(Nara Women Univ.).
https://forms.gle/QNj3fohg3ZRMD8RHA
2024/12/23
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Junjiro Noguchi (The Univ. of Tokyo)
Hyperbolicity and sections in a ramified cover over abelian varieties
with trace zero (Japanese)
https://forms.gle/gTP8qNZwPyQyxjTj8
Junjiro Noguchi (The Univ. of Tokyo)
Hyperbolicity and sections in a ramified cover over abelian varieties
with trace zero (Japanese)
[ Abstract ]
We discuss a higher dimensional generalization of the Manin-Grauert Theorem ('63/'65) in relation with the function field analogue of Lang's conjecture on the finiteness of rational points in a Kobayashi hyperbolic algebraic variety over a number field. Let $B$ be a possibly open algebraic curve over $\mathbf{C}$, and let $\pi:X \to B$ be a smooth or normal projective fiber space. In '81 I proved such theorems for $\dim \geq 1$, assuming the ampleness of the cotangent bundle $T^*(X_t)$, and in '85 the Kobayashi hyperbolicity of $X_t$ with some boundary condition (BC) (hyperbolic embedding condition relative over $\bar{B}$).
It is interesting to study if (BC) is really necessary or not. If $\dim X_t=1$, (BC) is automatically satisfied, and if $T^*(X_t)$ is ample, (BC) is not necessary; thus in those cases, (BC) is unnecessary. Lately, Xie-Yuan in arXiv '23 obtained such a result without (BC) for $X$ which is a hyperbolic finite cover of an abelian variety $A/B$.
The aim of this talk is to present a simplified treatment of the Xie-Yuan theorem from the viewpoint of Kobayashi hyperbolic geometry. In particular, if the $K/\mathbf{C}$-trace $Tr(A/B)=0$ with $K=\mathbf{C}(B)$, there are only finitely many $X(K)$-points or sections in $X \to B$. In this case, Bartsch-Javanpeykar in arXiv '24 gave another proof based on Parshin's topological rigidity theorem ('90). We will discuss the proof which is based on the Kobayashi hyperbolicity.
[ Reference URL ]We discuss a higher dimensional generalization of the Manin-Grauert Theorem ('63/'65) in relation with the function field analogue of Lang's conjecture on the finiteness of rational points in a Kobayashi hyperbolic algebraic variety over a number field. Let $B$ be a possibly open algebraic curve over $\mathbf{C}$, and let $\pi:X \to B$ be a smooth or normal projective fiber space. In '81 I proved such theorems for $\dim \geq 1$, assuming the ampleness of the cotangent bundle $T^*(X_t)$, and in '85 the Kobayashi hyperbolicity of $X_t$ with some boundary condition (BC) (hyperbolic embedding condition relative over $\bar{B}$).
It is interesting to study if (BC) is really necessary or not. If $\dim X_t=1$, (BC) is automatically satisfied, and if $T^*(X_t)$ is ample, (BC) is not necessary; thus in those cases, (BC) is unnecessary. Lately, Xie-Yuan in arXiv '23 obtained such a result without (BC) for $X$ which is a hyperbolic finite cover of an abelian variety $A/B$.
The aim of this talk is to present a simplified treatment of the Xie-Yuan theorem from the viewpoint of Kobayashi hyperbolic geometry. In particular, if the $K/\mathbf{C}$-trace $Tr(A/B)=0$ with $K=\mathbf{C}(B)$, there are only finitely many $X(K)$-points or sections in $X \to B$. In this case, Bartsch-Javanpeykar in arXiv '24 gave another proof based on Parshin's topological rigidity theorem ('90). We will discuss the proof which is based on the Kobayashi hyperbolicity.
https://forms.gle/gTP8qNZwPyQyxjTj8
2024/12/24
Tuesday Seminar of Analysis
16:00-17:30 Room #128 (Graduate School of Math. Sci. Bldg.)
KAKEHI Tomoyuki (University of Tsukuba)
Snapshot problems for the wave equation and for the Euler-Poisson-Darboux equation (Japanese)
https://forms.gle/2otzqXYVD6DqM11S8
KAKEHI Tomoyuki (University of Tsukuba)
Snapshot problems for the wave equation and for the Euler-Poisson-Darboux equation (Japanese)
[ Abstract ]
In this talk, we deal with snapshot problems for the wave equation and for the Euler-Poisson-Darboux equation. For simplicity, let us consider the wave equation $\partial_t^2 u - \Delta u =0$ on $\mathbb{R}^n$ with the condition $u|_{t=t_1} =f_1, \cdots, u|_{t=t_m} =f_m$. It is natural to ask when the above equation has a unique solution. We call the above problem the snapshot problem for the wave equation, and the set of $m$ functions $\{ f_1, \cdots, f_m \}$ the snapshot data. Roughly speaking, one of our main results is as follows.
Theorem. We assume that $m=3$ and $(t_3-t_1)/(t_2 -t_1)$ is irrational and not a Liouville number. In addition, we assume a certain compatibility condition on the snapshot data $\{ f_1, f_2, f_3 \}$. Then the snapshot problem for the wave equation has a unique solution.
We also consider a similar snapshot problem for the Euler-Poisson-Darboux equation. This is a joint work with Jens Christensen, Fulton Gonzalez, and Jue Wang.
[ Reference URL ]In this talk, we deal with snapshot problems for the wave equation and for the Euler-Poisson-Darboux equation. For simplicity, let us consider the wave equation $\partial_t^2 u - \Delta u =0$ on $\mathbb{R}^n$ with the condition $u|_{t=t_1} =f_1, \cdots, u|_{t=t_m} =f_m$. It is natural to ask when the above equation has a unique solution. We call the above problem the snapshot problem for the wave equation, and the set of $m$ functions $\{ f_1, \cdots, f_m \}$ the snapshot data. Roughly speaking, one of our main results is as follows.
Theorem. We assume that $m=3$ and $(t_3-t_1)/(t_2 -t_1)$ is irrational and not a Liouville number. In addition, we assume a certain compatibility condition on the snapshot data $\{ f_1, f_2, f_3 \}$. Then the snapshot problem for the wave equation has a unique solution.
We also consider a similar snapshot problem for the Euler-Poisson-Darboux equation. This is a joint work with Jens Christensen, Fulton Gonzalez, and Jue Wang.
https://forms.gle/2otzqXYVD6DqM11S8
2024/12/26
Discrete mathematical modelling seminar
15:00-17:00 Room #002 (Graduate School of Math. Sci. Bldg.)
Wookyung KIM (Graduate School of Mathematical Sciences)
Integrable deformation of cluster map associated to finite type Dynkin diagram
Wookyung KIM (Graduate School of Mathematical Sciences)
Integrable deformation of cluster map associated to finite type Dynkin diagram
[ Abstract ]
An integrable deformation of a cluster map is an integrable Poisson map which is composed of a sequence of deformed cluster mutations, namely, parametric birational maps preserving the presymplectic form but destroying the Laurent property, which is a necessary part of the structure of a cluster algebra. However, this does not imply that the deformed map does not arise from a cluster map: one can use so-called Laurentification, which is a lifting of the map into a higher-dimensional space where the Laurent property is recovered, and thus the deformed map can be generated from elements in a cluster algebra. This deformation theory was introduced recently by Hone and Kouloukas, who presented several examples, including deformed integrable cluster maps associated with Dynkin types A_2,A_3 and A_4. In this talk, we will consider the deformation of integrable cluster map corresponding to the general even dimensional case, Dynkin type A_{2N}. If time permits, we will review the deformation of the cluster maps of other finite type cases such as type C and D. This is joint work with Grabowski, Hone and Mase.
An integrable deformation of a cluster map is an integrable Poisson map which is composed of a sequence of deformed cluster mutations, namely, parametric birational maps preserving the presymplectic form but destroying the Laurent property, which is a necessary part of the structure of a cluster algebra. However, this does not imply that the deformed map does not arise from a cluster map: one can use so-called Laurentification, which is a lifting of the map into a higher-dimensional space where the Laurent property is recovered, and thus the deformed map can be generated from elements in a cluster algebra. This deformation theory was introduced recently by Hone and Kouloukas, who presented several examples, including deformed integrable cluster maps associated with Dynkin types A_2,A_3 and A_4. In this talk, we will consider the deformation of integrable cluster map corresponding to the general even dimensional case, Dynkin type A_{2N}. If time permits, we will review the deformation of the cluster maps of other finite type cases such as type C and D. This is joint work with Grabowski, Hone and Mase.
